International Conference: ///Analysis and PDEs on Manifolds000 · 2017-08-08 · Verbitsky, Igor...

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International Conference:

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.Nankai University, Tianjin

.September 21 to 23 , 2017

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This conference is organized jointly by the Nankai University (China) and Bielefeld U-niversity (Germany), and sponsored by Nankai University and SFB1283 of German Re-search Council.

We would like to attract to the conference experts working on different aspects ofPDEs on manifolds, including analytic, geometric and stochastic points of view, as wellas both linear and non-linear PDEs, as well as on geometric flows.

Scientific Committee

Bidaut-Veron, Marie-Francoise (University of Francois Rabelais, France)

Grigor’yan, Alexander (University of Bielefeld, Germany and Nankai University)

Hu, Jiaxin (Tsinghua University, China)

Hsu, Elton Pei (Northwestern University, USA)

Lin, Yong (Renmin University of China, China)

Long, Yiming (Nankai University, China)

Ni, Lei (University of California, San Diego, USA)

Rockner, Michael (University of Bielefeld, Germany)

Verbitsky, Igor (University of Missouri, USA)

Veron, Laurent (University of Francois Rabelais, France)

Xiao, Jie (Memorial University, Canada)

Zhang, Qi S. (University of California Riverside, USA)

Organizational Committee

Alexander Grigor’yan (University of Bielefeld and Nankai University)

Yuhua Sun (Nankai University, China)

Yawei Wei (Nankai University, China)

Longmin Wang (Nankai University, China)

Conference Homepage

http://sms.nankai.edu.cn/2017/0518/c5538a66867/page.htm

http://en.sms.nankai.edu.cn/2017/0524/c4029a67203/page.htm

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http://sms.nankai.edu.cn/2017/0518/c5538a66867/page.htm

http://en.sms.nankai.edu.cn/2017/0524/c4029a67203/page.htm

Contact information

Yuhua Sun (u) [email protected] Tel: (+86)18522707104

Yawei Wei (äv) [email protected] Tel: (+86)13920365027

Longmin Wang (9¯) [email protected] Tel: (+86)13802143032

Jianxin Li (oï#) [email protected] Tel: (+86)13752412809

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Schedule September 20, 2017

15:00-20:00 Registration: Minzhuyuan Hotel 明珠园宾馆大厅

17:00-19:30 Dinner： Jiayuan Hotel 嘉园一楼

September 21, 2017

Plenary talks 数学学院

8:45-9:00 开幕式 Opening Ceremony

Chairman Qi S. Zhang

9:00-9:50 Laurent Véron (University of Francois Rabelais)

Separable p-harmonic functions in a cone, 1<p≤ ∞

10:00-10:50 Yiming Long (Nankai University)

Closed geodesics on compact Finsler manifolds-A survey

10:50-11:20 Tea Break

11:20-12:10 Lei Ni (University of California)

Optimal solutions to Poincar\'e-Lelong equation and applications

12:10:14:00 Lunch: 美食广场三楼

chairman Yong Lin

14:00-14:50 Elton P. Hsu ( Northwestern University, USA and

University of Science and Technology of China)

Beckner's Inequality: From the Beginning to Yesterday

Section talks 数学学院

Place TBA TBA

Chairman Yong Lin Jie Xiao

15:00-15:40 Radoslaw Wojciechowski

(City University of New York)

Ollivier Ricci curvature and the heat

equation

Liguang Liu

(Renmin University of China)

Restricting

Riesz-Morrey-Hardy

Potentials

15:40-16:15 Tea Break

16:15-16:55 Bobo Hua

(Fudan University)

Some results on graphs with nonnegative

Bakry-Emery curvature

Janna Lierl

(University of Connecticut)

Neumann heat flow and

gradient flow for the entropy

on non-convex domains

17:00-17:40 Shiping Liu (University of Science and

Technology of China)

Magnetic sparseness and Schrodinger

operators on graphs

Satoshi Ishiwata

(Yamagata University)

Poincare inequality on

manifolds with ends


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September 22, 2017


Chairman Alexander Grigor’yan

9:00-9:50 Marie-Francoise Bidaut- Véron (University of Francois Rabelais)

A priori estimates and ground states of solutions of some

Emden-Fowler

equations with gradient term

10:00-10:50 Jie Xiao (Memorial University)

Q - Q−1 Spaces for Navier-Stokes Systems

10:50-11:20 Tea Break

11:20-12:10 Qi S. Zhang (University of California Riverside)

Bounds on harmonic radius and limits of manifolds with bounded

Bakry-Emery Ricci curvature

12:10-14:00 Lunch: 美食广场三楼

Chairman Jie Xiao

14:00-14:50 Igor Verbitsky (University of Missouri)

Global pointwise estimates and existence theorems for positive

solutions to

local and non-local elliptic PDE


Place TBA TBA

Chairman Laurent Véron Jiaxin Hu

15:00-15:40 Huyuan Chen

(Jianxi Normal University)

New distributional sense for the study of

Isolated singularities on Hardy

equations

Michael Hinz

(Bielefeld University )

Probabilistic

characterizations of essential

self-adjointness of

Laplacians

15:40-16:15 Tea Break

16:15-16:55 Yu Liu

(University of Science and Technology

Beijing)

Sub-Laplacian differential inequalities on

Heisenberg groups

Jun Masamune

(Tohoku University)

A conservation property of

Brownian motion with killing

of a Riemannian manifold

17:00-17:40 Chao Zhang

(Haerbin Institute of Technology)

The Gradient estimates for the

nonstandard quasilinear elliptic and

parabolic equations

Eryan Hu

(Tianjin University )

Two-sided estimates of heat

kernels of jump type

Dirichlet forms

18:00-20:00 Banquet：美食广场三楼

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September 23, 2017


Chairman Igor Verbitsky

9:00-9:50 Michael Röckner (Bielefeld University)

Existence and uniqueness of absolutely continuous solutions to

continuity

equations on Hilbert spaces

10:00-10:50 Jiaxin Hu (Tsinghua University)

Heat kernel estimates for local and non-local Dirichlet forms

10:50-11:20 Tea Break

11:20-12:10 Yong Lin (Renmin University of China)

Several Partial differential equations on graphs

12:10-14:00 Lunch: 美食广场三楼

Chairman Elton P. Hsu

14:00-14:50 Alexander Grigor’yan (Bielefeld University and Nankai University)

Heat kernels on ultra-metric spaces


Place TBA TBA

Chairman Yu Liu Michael Hinz

15:00-15:40 Qianqiao Guo

(Northwestern Polytechnical University)

Integral equations on bounded domains

related to the sharp reversed

Hardy-Littlewood-Sobolev inequality

Qingsong Gu

(The Chinese University of

Hong Kong)

On a recursive construction

of Dirichlet form on the

Sierpi nski gasket

15:40-16:15 Tea Break

16:15-16:55 Baiyu Liu

(University of Science and Technology

Beijing)

The radial symmetry results for fractional

Laplacian systems

Meng Yang

(Bielefeld University)

Local and Non-Local Dirichlet

Forms on the Sierpinski

Carpet

17:00-17:40 Yuhua Sun

(Nankai University)

On positive solutions

of semi-linear elliptic inequalities on

Riemannian manifolds

Shilei Kong

(The Chinese University of

Hong Kong)

Random walks and induced

Dirichlet forms on compact

doubling spaces


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A priori estimates and ground states of solutions of some Emden-Fowlerequations with gradient term

Bidaut-Veron, Marie-Francoise (University of Francois Rabelais, France)

Abstract: Here we consider the nonnegative solutions of equations in a punctured ballB(0, R)0 ⊂ RN or in RN of two types:

−∆u = up|∇u|q, for large r, (1)

and

−∆u = up +M |∇u|q, for large r, (2)

where p; q > 1 and q > 1 andM ∈ R. We give new a priori estimates on the solutions andtheir gradient, and Liouville type results. We use Bernstein technique and Osserman.sor Gidas-Spruck.s type methods. The most interesting cases correspond to q < 1 forequation (1) and q = 2p = (p+ 1) for equation (2)

New distributional sense for the study of Isolated singularities on Hardyequations

Chen, Huyuan (Jianxi Normal University, China)

Abstract: In this talk, we will discuss the isolated singularities of semilinear Hardyequation

−∆u+ µ|x|−2u = f.

in a new distributional sense, where f ∈ Cγloc(Ω \ 0).We give the some applications on the nonexistence of some nonhomogeneous problems

with the Hardy-Leray potentials and the nonexistence principle eigenvalue with someindefinite potentials.

Heat kernels on ultra-metric spaces

Grigor’yan, Alexander (Nankai University and Bielefeld University)

Abstract: We define a natural class of non-local Dirichlet forms on ultra-metric spacesand prove upper and lower estimates of the corresponding heat kernels.

On a recursive construction of Dirichlet form on the Sierpinski gasket

Gu, Qinsong (The Chinese University of Hong Kong, China)

Abstract: Let Γn denote the n-th level Sierpinski graph of the Sierpinski gasket K.We consider, for any given conductance (a0, b0, c0) on Γ0, the Dirchlet form E on Kobtained from a recursive construction of compatible sequence of conductances (an, bn, cn)on Γn, n ≥ 0. We prove that there is a dichotomy situation: either a0 = b0 = c0 and E is

Title and abstracts

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TITLES AND ABSTRACTS

the standard Dirichlet form, or a0 > b0 = c0 (or the two symmetric alternatives), and Eis a non-self-similar Dirichlet form independent of a0, b0. The second situation was firstcreated by [K.Hattori, T.Hattori, and H.Watanabe 1994] and later studied by [B.Hamblyand O.Jones 2002] as a one-dimensional asymptotic diffusion process on the Sierpinskigasket. For the spectral property, we give a sharp estimate of the eigenvalue distributionof the associated Laplacian.

Integral equations on bounded domains related to the sharp reversedHardy-Littlewood-Sobolev inequality

Guo, Qianqiao (Northwestern Polytechnical University, China)

Abstract: We introduce and study some new nonlinear integral equations on bound-ed domains that are related to the sharp reversed Hardy-Littlewood-Sobolev inequality.Existence results as well as non-existence results are obtained. This is a joint work withProf. Jingbo Dou and Prof. Meijun Zhu.

Probabilistic characterizations of essential self-adjointness of Laplacians

Hinz, Michael (Bielefeld University, Germany)

Abstract: We consider the Laplace operator on the complement of a given compactsubset of zero measure of a manifold. Depending on the size of this set the Laplace op-erator, equipped with the smooth compactly supported functions on the complement ofthe given subset, may or may not be essentially self-adjoint. It is well-known that thecritical size of the given subset can be described in terms of capacities and Hausdorff mea-sures, and we survey some of these results. Then we show that, although a priori essentialself-adjointness is not a notion directly related to classical probability, the critical size ofthe subset can also be characterized via Kakutani type theorems for certain stochasticprocesses. The presented results are joint with Jun Masamune (Sapporo) and partly jointwith Seunghyun Kang (Seoul).

Beckner’s Inequality:From the Beginning to Yesterday

Hsu, Elton P. ( Northwestern University, USA and University of Science and Technologyof China)

Abstract: Beckner’s inequality is a functional inequality which interpolates betweenthe Poincare inequality and the logarithmic Sobolev inequality. We will start with theoriginal Beckner’s inequality for the standard Gaussian measure aWe study Levy’s arcsinelaw near a hypersurface on a Riemannian manifold. The main result is that the deviationfrom the classical arcsine law is of the order of the square-root of time and can expressedexplicitly in terms of tnd graduate build its far-reaching extension to the Wiener measureon the path space over a complete Riemannian manifold of bounded Ricci curvature. Thelecture will culminiate in the latest Beckner’s inequality for time-dependent Riemannianmetric and the important role the Ricci flow in this context.

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Two-sided estimates of heat kernels of jump type Dirichlet forms

Hu, Eryan (Tianjin University, China)

Abstract: We prove necessary and sufficient conditions for the following stable-like esti-mates of the heat kernel for jump type Dirichlet forms on metric measure spaces:

pt(x, y) C

tα/β

(1 +

d(x, y)

t1/β

)−(α+β),

where in some cases α > 0 is the Hausdorff dimension and β > 0 is called the index ofthe associated jump process. The conditions are given in terms of the volume growthfunction, jump kernel and a generalized capacity. The main question that we address hereis obtaining equivalent conditions for the above estimate for arbitrary values of the indexβ, in particular, for β ≥ 2.

Heat kernel estimates for local and non-local Dirichlet forms

Hu, Jiaxin (Tsinghua University, China)

Abstract: I will give a short survey on heat kernel estimates for regular Dirichlet forms onmetric measure spaces. For a local Dirichlet from, the heat kernel admits sub-Gaussian orGaussian bound, whilst for a nonlocal one, its heat kernel admits stable-like bound. Thetalk is based on a series of papers with my collaborators Alexander Grigor’yan, Ka-SingLau, and Eryan Hu.

Some results on graphs with nonnegative Bakry-Emery curvature

Hua, Bobo (Fudan University, China)

Abstract: Recently, many geometric and analytic results on graphs have been obtained viaBakry-Emery type curvatures, e.g. Myers’ theorem and Lichnerowicz-Obata theorem forgraphs with curvature bounded below by a positive constant. In this talk, we will studysome properties of the graphs with nonnegative Bakry-Emery curvature. This is based onjoint works with Yong Lin and Florentin Munch.

Poincare inequality on manifolds with ends

Ishiwata, Satoshi (Yamagata University, Japan)

Abstract: Heat kernel estimates on manifolds with ends was obtained by Grigor’yanand Saloff-Coste (non-parabolic case) in 2009 and Grigor’ yan, Ishiwata and Saloff-Coste(parabolic case) in 2016. In this talk, based on the heat kernel estimates, we discussthe Poincare inequality on manifolds with ends. This talk is based on a joint work withAlexander Grigor’yan (Bielefeld) and Laurent Saloff-Coste (Cornell).

Random walks and induced Dirichlet forms on compact doubling spaces

Kong, Shilei (The Chinese University of Hong Kong, China)

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Abstract: For a compact doubling space K, there is a naturally defined augmented treestructure (X,E) associated with a “tree partition” on K that is Gromov hyperbolic. Weconsider certain reversible random walks on (X,E) so that the Martin boundary can beidentified with the hyperbolic boundary and K. Asymptotic estimates of the Martin kerneland the Naım kernel are obtained, which provides the order of the Dirichlet form inducedby the random walk. This is a joint work with Ka-Sing Lau and Ting-Kam Leonard Wong.

Neumann heat flow and gradient flow for the entropy on non-convex domains

Lierl, Janna (University of Connecticut, USA)

Abstract: For large classes of non-convex subsets Y in Rn or in Riemannian manifolds orin RCD-spaces (X, d,m), we prove that the gradient flow of the Boltzmann entropy on therestricted metric measure space (Y, dY ,mY ) exists - despite the fact that the entropy is notsemiconvex - and coincides with the heat flow on Y with Neumann boundary conditions.This is joint work with K.-T. Sturm.

Several Partial differential equations on graphs

Lin, Yong (Renmin University of China, China)

Abstract: We will study the solutions of several Partial differential equations on graphs.These Partial differential equations include the Variational Inequalities, Yamabe equations,Karzan-Warner equations and semilinear heat equations. These are serial joint works withGrigor’yan, Horn, Wu, Yang and Yau.

The radial symmetry results for fractional Laplacian systems

Liu, Baiyu (University of Science and Technology Beijing, China)

Abstract: In this talk, we consider the fractional Laplacian system. By generalizing thedirect method of the moving planes to the system case, we obtain two radial symmetryresults for the decaying solutions of the fractional system.

Restricting Riesz-Morrey-Hardy Potentials

Liu, Liguang (Renmin University of China, China)

Abstract: Let µ be a non-negative Radon measure on the n-dimensional Euclidean spaceRn. In this talk, we shall use a geometric-measure-theoretic criterion on the measure µto characterize the boundedness of the Riesz potential Iα of order α ∈ (0, n) from Morreyor Hardy-Morrey spaces to the µ-based Radon-Morrey or µ-based Radon-Hardy-Morreyspaces. This work is jointed with Professor J. Xiao.

Magnetic sparseness and Schrodinger operators on graphs

Liu, Shiping (University of Science and Technology of China)

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Abstract: We discuss magnetic Schrodinger operators on graphs in this talk. We extendthe notion of sparseness of graphs by including a magnetic quantity called the frustrationindex. This notion of magnetic sparse turn out to be equivalent to the fact that the formdomain is an `2 space. As a consequence, we get criteria of discreteness for the spectrumand eigenvalue asymptotics. This is based on a joint work with Michel Bonnefont, SylvainGolenia, Matthias Keller, and Florentin Munch.

Sub-Laplacian differential inequalities on Heisenberg groups

Liu, Yu (University of Science and Technology Beijing, China)

Abstract: In this talk we introduce the nonnegative solutions of

(†) ‖g|γHnup ≤ (−∆Hn)α2 u on Hn,

where Hn is the Heisenberg group; | · |Hn is the homogeneous norm; ∆Hn is the sub-Laplacian; (p, α, γ) ∈ (1,∞) × (0, 2) × [0, (p − 1)Q); and Q = 2n + 2 is the homogeneousdimension of Hn. In particular, we prove that any nonnegative solution of (†) is zero if

and only if p ≤ Q+γQ−α .

Closed geodesics on compact Finsler manifolds-A survey

Long, Yiming (Nankai University, China)

Abstract: The problem of closed geodesics on Riemannian manifold is a classical topic indynamical systems and differential geometry. In 1973 A. Katok constructed a family ofsurpricing Finsler metrics on n-dimensional spheres which possesse precisely 2[(n+ 1)/2]distinct closed geodesics. Then D. Anosov conjectured in ICM-1974 that on any Finslern-sphere, there should always exist at least 2[(n + 1)/2] distinct closed geodesics. Thisconjecture was proved by V. Bangert and the author jointly for dimension 2 in 2004(published in Math. Ann. in 2010). Since then many deep research results on this topichave appeared. In this talk, I shall give a survey on the related new progress obtainedsince 2004.

A conservation property of Brownian motion with killing of a Riemannianmanifold

Masamune, Jun (Tohoku University, Japan)

Abstract: We study a new type of conservation property of Brownian motion withkilling of a Riemannian manifold, which is an extension of the discrete version introducedby Keller and Lenz. The main result was obtained on a joint work with Marcel Schmidt.

Optimal solutions to Poincare-Lelong equation and applications

Ni, Lei (University of California, San Diego, USA)

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Abstract: Poincare-Lelong equation is a over-determined equation on complex mani-folds. Its relevance to geometry was first established by Mok-Siu-Yau. In a joint work withTam we developed a parabolic method to obtain solutions with sharp estimates. Sincethen some application of the solution was obtained by Gang Liu in his recent works. Thissolution can also be used to prove a new gap theorem. This last part is a recent joint workwith Yanyan Niu and Luen-Fei Tam.

Existence and uniqueness of absolutely continuous solutions to continuityequations on Hilbert spaces

Rockner, Michael (Bielefeld University, Germany)

Abstract: TBA.

On positive solutions of semi-linear elliptic inequalities on Riemannianmanifolds

Sun, Yuhua (Nankai University, China)

Abstract: We determine the critical exponent for certain semi-linear elliptic problemon a Riemannian manifold assuming the volume regularity and Green function estimates.This is a recent joint work with Prof. A. Grigor’yan.

Global pointwise estimates and existence theorems for positive solutions tolocal and non-local elliptic PDE

Verbitsky, Igor (University of Missouri, Columbia, USA)

Abstract: Sharp global pointwise estimates will be presented for positive solutions toelliptic equations of the type −∆u+ σ uq = µ, for all real q 6= 0, where σ, µ are functions,or measures, on a domain Ω ⊆ Rn, or a weighted Riemannian manifold (M,ω), and∆ = divω · ∇, divω = 1

ω div ω is the weighted Laplacian on (M,ω).Analogues of these estimates for nonlocal operators of the fractional Laplacian type, as

well as integral operators with positive kernels satisfying various forms of the maximumprinciple will be discussed. In some cases, necessary and sufficient conditions for theexistence of positive solutions will be presented. This talk is based on joint work withMichael Frazier and Fedor Nazarov, and Alexander Grigor’yan.

Separable p-harmonic functions in a cone, 1 < p ≤ ∞

Veron, Laurent (University of Francois Rabelais, France)

Abstract: We study the existence of p-harmonic functions in a cone CS = S × (0,∞),where S is a subdomain of SN−1, vanishing on ∂CS\0 under the form u(r, σ) = r−βω(σ).

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When 1 < p <∞, ω verifies

div′((β2ω2 + |∇′ω|2

) p−22 ∇′ω

)+ Λ(β)

(β2ω2 + |∇′ω|2

) p−22 ω = 0, in S,

ω = 0, on ∂S,(0.1)

where Λ(β) = β(β(p− 1) + p−N). When p =∞, ω satisfies (in the viscosity sense)12∇′|∇′ω|2.∇′ω + β(2β + 1)|∇′ω|2ω + β3(β + 1)ω3 = 0 in Sω = 0 on ∂S.

(0.2)

Existence and uniqueness (up to an homothety) is known for (0.1) for smooth domains(P. Tolksdorf, 1984). In a joined work with K. Gkikas we prove existence in any sphericaldomain and obtain uniqueness (up to an homothety) in Lipschitz domain, and the proofheavily relies on the characterization of the p-Martin boundary by Lewis and Nystrom.For (0.2) existence in 1D is due to T. Bhattacharya. In a joined work with M.F. Bidaut-Veron and M. Garcia-Huidobro, we obtain existence in any dimension and any sphericaldomain.

Ollivier Ricci curvature and the heat equation

Wojciechowski, Radoslaw (York College of the City University of New York, USA)

Abstract: We extend the definition of Ollivier Ricci curvature to the case of generalgraph Laplacians. This allows us to study new phenomena which arises in the case ofunbounded operators. In particular, we give optimal curvature criteria for stochasticcompleteness and for finiteness of the graph. This is joint work with Florentin Munch.

Q−Q−1 Spaces for Navier-Stokes Systems

Xiao, Jie (Memorial University, Canada)

Abstract: This talk will address not only the geometric-function-theoretic properties ofQ space in several real variables (introduced in 2000 by Essen-Janson-Peng-Xiao) andits divergence form Q−1 = div(Q, ,,Q) but also their applications in the incompressibleNavier-Stokes systems.

Local and Non-Local Dirichlet Forms on the Sierpinski Carpet

Yang, Meng (Bielefeld University, Germany)

Abstract: We give a purely analytic construction of a self-similar local regular Dirichletform on the Sierpinski carpet using approximation of stable-like non-local closed formswhich gives an answer to an open problem in analysis on fractals. This is a joint workwith Alexander Grigor’yan (Bielefeld).

The Gradient estimates for the nonstandard quasilinear elliptic and parabolicequations

Zhang, Chao (Haerbin Institute of Technology, China)

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Abstract: In this talk, I present some new gradient estimates in different functional spacesfor weak solutions of some quasilinear elliptic and parabolic equations with non-standardgrowth.

Bounds on harmonic radius and limits of manifolds with boundedBakry-Emery Ricci curvature

Zhang, Qi S. (University of California Riverside, USA)

Abstract: Under the usual condition that the volume of a geodesic ball is close to theEuclidean one, we prove a lower bound of the Cα ∩W 1,q harmonic radius for manifoldswith bounded Bakry-Emery Ricci curvature when the gradient of the potential is bounded.This is almost 1 order lower than that in the classical C1,α ∩W 2,p harmonic coordinatesunder bounded Ricci curvature condition. The method of proof can also be used to addressthe detail of W 2,p convergence in the classical case, which seems not in the literature.

Based on this lower bound and the techniques in Cheeger and Naber and F. Wangand X.H. Zhu, we extend Cheeger-Naber’s Codimension 4 Theorem to the case where themanifolds have bounded Bakry-Emery Ricci curvature when the gradient of the potentialis bounded. This result covers Ricci solitons when the gradient of the potential is bounded.Some short cuts and additional information in the original case are also obtained. This isjoint work with Zhu Meng.

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Travel Information

Options of traveling to Nankai University, Tianjin:

1. Fly to Tianjin airport. Tianjin airport (TSN) has direct flights from all majorcities within Mainland China, as well as direct flights from Taipei, Hong Kong,Seoul, Osaka, Nagoya. The ground transportation from Tianjin airport to Nankaicampus is usually by Taxi, which is about 40 minute for 23-25 km (in normal traffic),cost about 60-80 Yuan. You can also take Tianjin Metro Line 2 from airport intocity then transfer to taxi. The Tianta Station (U©Õ) on Metro Line 3 is about1.5km from Nankai University.

2. Fly to Beijing airport. Beijing airport (PEK) is one of world.s largest airportswith flights from almost all major airports around the world. PEK is about 160kmaway from Nankai campus. The best way to arrive at Nankai campus from PEKis to take the airport shuttle from PEK to Tianjin (82 Yuan), and it takes about2.5-3 hours depending on traffic(without stop, so if can not bear long travel, werecommend to take the trains from Beijing south station to Tianjin station, seeoption 3.). The shuttle leaves Beijing airport every 30-45 minutes in daytime. Afterarriving Tianjin, you can take a Taxi to Nankai University (about 15-20 Yuan).

3. Take trains. You can take high speed train from Beijing South Station(®HÕ) to Tianjin Station £U9Õ¤(in the city, 8-10km), which costs 55 (2nd class)or 66 (1st class) Yuan and it takes about 30-35 minutes.

IF you want to buy the train tickets in Beijing South station(®®®HHHÕÕÕ),you can show the following Chinese characters:

···ïïïUUU999ÕÕÕ»»»¦¦¦§§§

which means that I want to buy train tickets to Tianjin Station.

4. Tianjin Metro. You can take Tianjin Metro from airport (Line 2 to Line 3),railway station (Line 3) to a station near Nankai University. The Tianta Stationon Metro Line 3 is about 1.5km from Nankai University. The metro ticket is 3-5Yuan.

5. Take taxi. From any place in Tianjin to Nankai University, if you want to taketaxi, you can show the following Chinese characters:

···HHHmmmÆÆÆlllppp«««EEExxx´þþþHHH£££±±±ooonnn@@@>>>¤¤¤§§§

which means that I want to go to south gate of Nankai University.

Map from Tianta Station (Exit B) on Metro Line 3 to Mingzhuyuan Hotel and JiayuanHotel on the South gate of Nankai University. From there, it is about 15 minutes walkto the Hotel.

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Advice: If you come from abroad, please have your currency exchanged before arrivalor at the airport. The local transportation services only take Chinese Yuan (RMB). Ofcourse, you can exchange for RMB at Bank of China anywhere in China . Please bringyour passport when you make the exchange. Banks and their airport branches are theonly legal money exchange authorities in China .

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Participants List

No. Name Affliations E-mails

1.Bidaut-Veron,

Marie-FrancoiseUniversity of Francois

Rabelais, [email protected]

2. Chen, huyuanJianxi Normal University,

[email protected]

3. Chen, YouminUniversity of Science and

Technology of [email protected]

4. Cheng, LiangCentral China Normal

University, [email protected]

5. Du, RunmeiChangchun University of

Technology, Chinadurm [email protected]

6. Gu, QingsongThe Chinese University of

Hongkong, [email protected]

7. Guo, QianqiaoNorthwestern Polytechnical


8.Grigor.yan,

Alexander

University of Bielefeld,Germanyand Nankai


9. Hinz, MichaelUniversity of Bielefeld,

[email protected]

10. Hu, EryanUniversity of Bielefeld,

[email protected]

11. Hu, Jiaxin Tsinghua University, China [email protected]

12. Hua, bobo Fudan University, China [email protected]

13. Huang, YiNanjin Normal University,

[email protected]

14. Huang, XuepingNanjing University of

Information Science andTechnology, China

[email protected]

15. Hsu, Elton PeiNorthwestern University,

[email protected]

16.Ishiwata,Satoshi

Yamagata University,Japan

[email protected]

17. Ji, DeshengHeilongjiang University,

[email protected]

18. Jia, HuicaiRenmin University of

China, Chinahcjia@ruc,edu,cn

19. Ju, XueweiCivil Aviation University

Of [email protected]

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20. Kong, ShileiThe Chinese University of

Hongkong, [email protected]

21. Lan, Jingfen Xidian University, China [email protected]

22. Li, Chunqiu Tianjin University, China [email protected]

23. Li, Haoyu Tianjin University, China [email protected]

24. Lierl, JannaUniversity of Connecticut,

[email protected]

25. Lin, YongRenmin University of

China, [email protected]

26. Liu, BaiyuUniversity of Science

Technology Beijing, [email protected]

27. Liu, LiguangRenmin University of

China, [email protected]

28. Liu, Qiang Tianjin University, China [email protected]

29. Liu, YuUniversity of Science

Technology Beijing, [email protected]

30. Liu, ShipingUniversity of Science and

Technology of [email protected]

31. Liu, Shuang Tsinghua University, China [email protected]

32. Long, Yiming Nankai Univeristy, China [email protected]

33. Lu, JianZhejiang University of

Technology, [email protected]

34. Lv, YuemingHaerbin University of

Science and Technology,China

35. Masamune, Jun Tohoku University, Japan [email protected]

36. Ni, LeiUniversity of California,

[email protected]

37. Peng, Xue Sichuang University, China [email protected]

38.Rockner,Michael

University of Bielefeld,Germany

[email protected]

39. Shen, Cong Tianjin University, China [email protected]

40. Sun, Wenchang Nankai University, China [email protected]

41. Sun, Yuhua Nankai University, China [email protected]

42. Song, Xianfa Tianjin University, China [email protected]

43. Verbitsky, IgorUniversity of Missoruri,

[email protected]

44. Veron, LaurentUniversity of

Francois-Rabelais, [email protected]

tours.fr

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45. Wang, JintaoHuazhong University ofScience and Technology,

[email protected]

46. Wang, JunCapital Normal University,

ChinaJida [email protected]

47. Wang, LifeiHebei Normal University,

[email protected]

48. Wang, LinChangchun University of


49. Wang, longming Nankai University, China [email protected]

50. Wang, YuzhaoNorth China Electric

Power University, [email protected]

51. Wang, ZhaoChangchun University of


52. Wei, Yawei Nankai University, China [email protected]

53. Wu, Weina Nankai University, China [email protected]

54. Wu, YitingRenmin University of

China, Chinayitingwu@ruc,edu,cn

55.Wojciechowski,

Radek

York College of the CityUniversity of New York,

[email protected]

56. Xiang, Kainan Nankai University, China [email protected]

57. Xiao, JieMemorial University,

[email protected]

58. Xu, Fanheng Nankai University, China [email protected]

59. Yang, Chao Walter de Gruyter GmbH [email protected]

60. Yang, MengUniversity of Bielefeld,

[email protected]

61. Zhang, ChaoHarbin Institute ofTechnology, China

[email protected]

62. Zhang, Qi S.University of California

Riverside, [email protected]

63. Zhang, Zhenqiu Nankai University, China [email protected]

64. Zhao, GuohuanAcademy of Mathematics

and Systems Science, [email protected]

65. Zhou, Luyan Tianjin University, China [email protected]

66. Zhu, Anqiang Wuhan University, China [email protected]

67.

68.

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International Conference: ///Analysis and PDEs on Manifolds000 · 2017-08-08 · Verbitsky, Igor...

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