A sharp lower bound for the first (nonzero) Steklov eigenvalue

发布时间：2021-06-21 作者：77779193永利官网浏览次数：

Speaker:	夏超	DateTime:	2021年6月24日（周四）下午14:00-15:00
Brief Introduction to Speaker: 夏超，华中师范大学教授。		Place:	线上会议（会议地址请联系程亮老师获取）
Abstract:Escobar has conjectured that for a compact manifold with boundary which has nonnegative Ricci curvature and boundary principal curvatures bounded below by 1, the first (nonzero) Steklov eigenvalue is greater than or equal to 1，with equality holding only on a Euclidean ball. This conjecture is true in two dimensions 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. We will also give a sharp comparison result between the first (nonzero) Steklov eigenvalue and the boundary first eigenvalue. Our tool is a weighted Reilly type formula due to Qiu-Xia and a Pohozaev type identity. The talk is based on a joint work with Changwei Xiong.