The first Dirichlet eigenvalue and the width
数学专题报告
报告题目(Title)：The first Dirichlet eigenvalue and the width
报告人(Speaker)：徐国义（清华大学）
地点(Place)：后主楼1124
时间(Time)：2023年11月16日，10：00—11：30
邀请人(Inviter)：熊金钢
报告摘要
In this talk, we present a quantitative inequality linking with the first Dirichlet eigenvalue and the width of the domain. Specifically, this inequality gives the upper bound of the width of any geodesic ball with non-negative Ricci curvature and mean convex boundary, in the form of the gap between the first Dirichlet eigenvalue of this geodesic ball and its sharp lower bound. The proof starts from one new equation of eigenvalue and ‘model’ function, and relies on Stable Gou-Gu Theorem on manifolds with non-negative Ricci curvature. In the first part of the talk, I will present the related historical results and motivation for our problem. In the second part of the talk, we will present some technical key points of our proof with suitable details.
The talk will be in blackboard.
