Thematic Session 2: Curvature Flows and Geometric Inequalities

Inverse mean curvature flow and Steklov eigenvalue in hyperbolic space

Haizhong Li
Tsinghua University
Peoples Rep of China
Co-Author(s):    
Abstract:
In this talk, by inverse mean curvature flow we establish optimal Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space $H^n$ . In particular, when the domain is convex, we give an affirmative answer to an open question by Colbois-Girouard-Gordon-Sher.