报告题目：A sharp lower bound for Steklov eigenvalues

报告人：夏超 教授（厦门大学）

时间：2019-10-18（周五）下午 4:00-5:00

地点：数学实验室

摘要：Lichernowicz-Obata’s theorem says that for a closed manifold with $Ric\ge (n-1)k>0$, the first (nonzero) eigenvalue is greater than or equal to $nk$,with equality holding only on a round sphere. Similar results for the first Dirichlet eigenvalue and Neumann eigenvalue have been shown by Reilly, Escobar and C.Y.Xia respectively. For the first (nonzero) Steklov eigenvalue, there is a conjecture by Escobar saying that for a compact manifold with boundary which has nonnegative Ricci curvature and boundary principal curvatures bounded below by some $c>0$, the first (nonzero) Steklov eigenvalue is greater than or equal to $c$，with equality holding only on a Euclidean ball. This conjecture is true in two dimension due to Payne and Escobar. In this talk, we present a resolution to this conjecture in the case of nonnegative sectional curvature in any dimensions. This is a joint work with Changwei Xiong.

报告人简介：夏超，厦门大学教授。2007年本科毕业于四川大学，2012年在德国弗莱堡大学取得博士学位，之后在德国应用数学马普所和加拿大麦吉尔大学从事博士后研究。他的主要研究领域是几何分析与非线性偏微分方程，研究成果发表在 JDG, Math. Ann., Adv. Math., IMRN, CVPDE, JGA, CAG等数学期刊上。