Speaker: Jingbo Wan（Columbia University）

Time: 09:00-10:00 a.m., March 6, 2024, GMT+8

Venue: Zoom: Link：https://us02web.zoom.us/j/83489104525?pwd=ZGRQb3VMRE9kNVhpem5qRE9DQXFkUT09; Meeting ID: 834 8910 4525; Passcode: 783607

Abstract: 

In this talk, we discuss the approach of Mean Curvature Flow to demonstrate that area non-increasing maps between certain positively curved closed manifolds are rigid. Specifically, this implies that an area non-increasing self-map of CPn,n≥2, is either homotopically trivial or is an isometry, answering a question by Tsai-Tsui-Wang. Moreover, by coupling the Mean Curvature Flow for the graph of a map with Ricci Flows for the domain and the target, we can also study the rigidity of area non-increasing maps from closed manifolds with positive 1-isotropic curvature (PIC1) to closed Einstein manifolds, where Prof. Brendle's PIC1 Sphere Theorem is applied. The key to studying the rigidity of area non-increasing maps under various curvature conditions lies in the application of the Strong Maximum Principle along the MCF/MCF-RF. We will focus our attention on one particular case to illustrate the SMP argument. This is a joint work with Professor Man-Chun Lee and Professor Luen-Fai Tam from CUHK.

Source: School of Mathematical Sciences, PKU