报告1
报告题目：On hypersurfaces in hyperbolic space
报告时间：2018年7月6日（星期五）09:00—09:45
报告地点：苏州大学本部精正楼211
报告人：Jie Qing (UC Santa Cruz)
报告提要：In this talk I will report our recent works on convex hypersurfaces in hyperbolic space. To study hypersurfaces in hyperbolic space analytically, one needs to find ways to parametrize it, preferably globally. We consider two parametrizations: vertical graph and hyperbolic Gauss map. To get a global parametrization, one needs understand the interrelation of convexity and embeddedness. It is also important to understand the asymptotic of the geometry at ends. In this talk I will report some of our recent works on global and asymptotic properties of hypersurfaces with nonnegative sectional curvature or Ricci curvature in hyperbolic space, where our use of n-Laplace equations seems to be new.
报告2
报告题目：Minimizers of the sharp Log entropy on manifolds with non-negative Ricci curvature and flatness
报告时间：2018年7月6日（星期五）10:15—11:00
报告地点：苏州大学本部精正楼211
报告人：Qi S. Zhang (UC Riverside & Fudan University)
报告提要：Consider the scaling invariant, sharp log entropy (functional) introduced by Weissler on noncompact manifolds with nonnegative Ricci curvature. It can also be regarded as a sharpened version of Perelman's W entropy in the stationary case. We prove that it has a minimizer if and only if the manifold is isometric to the Euclidean space. Using this result, it is proven that a class of noncompact manifolds with nonnegative Ricci curvature is isometric to R^n. Comparing with earlier well known flatness results on asymptotically flat manifolds and asymptotically locally Euclidean (ALE) manifolds, their decay or integral condition on the curvature tensor is replaced by the condition that the metric converges to the Euclidean one in C^1 sense at infinity. No second order condition on the metric is needed.
报告3
报告题目：Comparison and rigidity results on compact Riemannian manifolds with boundary
报告时间：2018年7月6日（星期五）11:10—11:55
报告地点：苏州大学本部精正楼211
报告人：Xiaodong Wang (Michigan State University)
报告提要：For compact Riemannian manifolds with nonempty boundary, it is interesting to study the relationship between the geometry on the boundary and geometry of the interior. I will discuss comparison and rigidity results for manifolds with a lower bound for the Ricci curvature. The focus will be on sharp geometric inequalities that yield rigidity results in the equality case.
报告4
报告题目：On the decay of the off-diagonal Bergman kernel on complete Kähler manifold
报告时间：2018年7月6日（星期五）14:00—14:45
报告地点：苏州大学本部精正楼211
报告人：Zhiqin Lu (UC Irvine)
报告提要：We give Agmon-type exponential estimates of the Bergman kernel for non-compact manifolds with different curvature bound assumptions, but without the non-collapsing condition of the volume. This is joint with Shoo Seto.
报告5
报告题目：On uniform estimate of the complex Monge-Ampère equation
报告时间：2018年7月6日（星期五）14:55—15:40
报告地点：苏州大学本部精正楼211
报告人：Bin Zhou (Peking University)
报告提要：In this talk, I will first review results on the uniform estimate of the complex Monge-Ampère equation, especially the famous proof of Kolodziej by using capacity theory. Then I will present a PDE proof by using Sobolev inequalities for the complex Monge-Ampère equation, which answers a question of Blocki-Kolodziej.
报告6
报告题目：Obata’s Rigidity theorem on manifolds with boundary
报告时间：2018年7月6日（星期五）16:10—16:55
报告地点：苏州大学本部精正楼211
报告人：Fang Wang (Shanghai Jiao Tong University)
报告提要：In this talk, I will introduce the rigidity theorem for Obata equation on manifolds with boundary with Robin boundary condition. Some application will also be given. This is joint work with Mijia Lai and Xuezhang Chen.
报告7
报告题目：Monge-Ampère equations on the sphere
报告时间：2018年7月6日（星期五）17:05—17:50
报告地点：苏州大学本部精正楼211
报告人：Qi-Rui Li (Australian National University)
报告提要：There are a number of geometric problems which can be reduced to the study of the Monge-Ampère equation on the sphere, including the Aleksandrov problem, the Minkowski problem, and more generally the L_p dual Minkowski problem. In this talk we give a brief discussion on these problems.