Workshop on geometric analysis

会议地点：浙江大学玉泉校区邵逸夫工商管理楼四楼会议室

时间：10月26日下午

14:00-14:50李嘉禹 Canonical metrics on reflexive sheaves

15:00-15:50 史宇光 Uniqueness of isoperimetric surfaces in asymptotically hyperbolic manifolds

16:00-16:50 麻希南 Parabolic Hessian equation with Neumann boundary value problem

会议联系人：盛为民教授shengweimin@zju.edu.cn

浙江大学数学学院

2018.10.23

题目与摘要(Title and abstract)

李嘉禹（中国科技大学教授）

Title: Canonical metrics on reflexive sheaves

Abstract: We will first recall the stability of vector bundles and Donaldson-Uhlenbeck-Yau theorem. Then we will talk about the existence of the canonical metrics, Bogomolov type inequalities and the limiting behavior of the Hermitian-Yang-Mills flow on reflexive sheaves. These are joint with Xi Zhang and Chuanjing Zhang.

史宇光（北京大学教授）

Title: Uniqueness of isoperimetric surfaces in asymptotically hyperbolic manifolds

Abstract: Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary.  It is interesting to see that some of quasi-local masses, like Brown-York mass, Hawking mass and isoperimetric mass have deep relation with classical isoperimetric inequality in asymptotically flat (hyperbolic)  manifolds.  In this talk, I will discuss these relations and finally give an application in the uniqueness of isoperimetric surfaces in asymptotically Ads-Schwarzschilds manifold with scalar curvature. This talk is based on my recent joint works with  M.Echmair, O.Chodosh and my Ph.D student J. Zhu .

麻希南（中国科技大学教授）

Title: Parabolic Hessian equation with Neumann boundary value problem

Abstract: In recently Hessian equation with Neumann boundary value problem was studied by Ma-Qiu and Chen-Zhang. We study the parabolic Hessian equation on convex domain with Neumann boundary value problem, and we prove the solution convergence to the translate solution. This is the joint work with Chen Chuanqiang and Zhang Dekai.