浙大-西湖几何分析讨论班——Weighted geometric inequalities and applications

Abstract:

In this talk, we discuss some weighted geometric inequalities for domains in space forms. First, we consider a weighted isoperimetric inequality which compares boundary momentum, boundary area and enclosed volume for a star-shaped and mean convex domain in the Euclidean space. As an application, we prove the Weinstock type inequality on the first non-zero Steklov eigenvalue for such domains. Second, we consider the weighted Alexandrov-Fenchel type inequalities which involve weighted curvature integrals and quermassintegrals for domains in space forms. For the proof, we used inverse curvature flows. The talk is based on some joint work with Yingxiang Hu, K.-K. Kwong, Haizhong Li and Tailong Zhou.