题目：Curvature integrals, curvature flows and geometric inequalities for hypersurfaces in space forms

报告人：夏超博士（德国leipzig马普数学所）

时间：

4月1日（周二）    14：00-16:30

4月2日（周三）    9:00-11：30

4月4日（周五）    9:00-11:30

地点：管理科研楼1516

摘要: In these lectures, we first introduce several important geometric quantities  for hypersurfaces in space forms from pointview of both  differential geometry and integral geometry. Precisely, we study the mean curvature integrals, the Gauss-Bonnet curvature integrals, the quermassintegrals and their relations. Then we introduce the method of using geometric flows to derive geometric inequalities. We give several examples for this method and give beautiful proofs of  several geometric inequalities, such as isoperimetric inequality. Last, we study carefully  a quermassintegral preserving curvature flow in the hyperbolic space and prove its  long time existence and convergence. We use such flow to prove new Alexandrov-Fenchel inequalities for horoconvex hypersurfaces in the hyperbolic space.

主办单位：我校研究生院
         我校数学学院

欢迎感兴趣的师生参加！