Speaker: Guoyi XU（Tsinghua University）

Time： April 6, 10:00-11:00

腾讯会议ID：981-472-543 密码：202204

Title： The sharp estimates of functions and the related rigidity, stability

Abstract： Since Cheng-Yau proved the gradient estimate of harmonic functions in 1975, their method played important role in geometric analysis. Its philosophy was generalized to prove the lower bound of eigenvalues and parabolic Harnack estimate by Li-Yau. In this talk, we will discuss the sharp gradient estimate for harmonic functions, sharp Dirichlet eigenvalues in geodesic ball. Furthermore, we present the corresponding sharp estimate for Green's function and heat kernel, and the rigidity and stability of those estimates will also be discussed. This is a survey report based on my former work and the joint work with Haibin Wang---Jie Zhou, and Qixuan Hu----Chengjie Yu. Only basic Riemannian geometry and PDE knowledge is enough to understand most part of the talk.