Spectral properties and rigidity for self-expanding solutions of the mean curvature flows

题目:Spectral properties and rigidity for self-expanding solutions of the mean curvature flows

报告人:程旭 教授,Universidade Federal Fluminense

时间:2018年7月19日 16:00-17:00

地点:知新楼B座1032

邀请人:张晓燕教授

Abstract:In this talk, we will discuss self-expanders which are the self-expanding solutions for mean curvature flows. We give a universal lower bound of the bottom of the spectrum of the drifted Laplacian and prove that the Euclidean subspace through the origin is the unique self-expander so that this lower bound is achieved. Further, for self-expander hypersurfaces, we prove an inequality between the bottom of the spectrum of the drifted Laplacian and the bottom of the spectrum of weighted stability operator and discuss the case that the equality holds.