浙江大学数学科学学院九十周年院庆系列活动之几何分析研讨会

几何分析研讨会

Workshop on geometric analysis

时间：10月26日下午

14:00-14:50李嘉禹 Canonicalmetrics on reflexive sheaves

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

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

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 ofvector bundles and Donaldson-Uhlenbeck-Yau theorem. Then we will talk about theexistence of the canonical metrics, Bogomolov type inequalities and thelimiting behavior of the Hermitian-Yang-Mills flow on reflexive sheaves. Theseare joint with Xi Zhang and Chuanjing Zhang.

史宇光（北京大学教授）

Title: Uniqueness of isoperimetric surfaces in asymptotically hyperbolicmanifolds

Abstract: Quasi-localmass is a basic notion in General Relativity. Geometrically, it can be regardedas a geometric quantity of a boundary of a 3-dimensional compact Riemannianmanifold. Usually, it is in terms of area and mean curvature of theboundary.  It is interesting to see that some of quasi-local masses, likeBrown-York mass, Hawking mass and isoperimetric mass have deep relationwith classical isoperimetric inequality in asymptotically flat(hyperbolic)  manifolds.  In this talk, I will discuss theserelations and finally give an application in the uniqueness of isoperimetricsurfaces 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 withNeumann boundary value problem

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