ABSTRACT

It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. I will present some recent progress on this question, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov), as well as complete metrics of positive scalar curvature on an arbitrary manifold connect sum with a torus. Applications include a Schoen-Yau Liouville theorem for all locally conformally flat manifolds. The proof of these results are based on analyzing generalized soap bubbles - surfaces that are stable solutions to the prescribed mean curvature problem. This talk is based on joint work with O. Chodosh.

ZOOM INFO

ID: 665 3312 8570

Password: 825477

https://zoom.com.cn/j/66533128570?pwd=d1llLzJ4RkYxZmFpR0tZSkQzM25wUT09

BRIEF BIO

Dr. Chao Li is currently an instructor at Department of Mathematics, Princeton University. Li received his undergraduate education at Peking University, where he was mentored by Huijun Fan. He received his Ph.D from Stanford University with his dissertation being supervised by Rick Schoen and Brian White. His research interests lie primarily in differential geometry, partial differential equations and geometric measure theory. His recent works focus on applications of geometric variational methods in the study of scalar curvature.

For more information about this seminar, please see below.

【Wednesday Online Seminar on Geometric Analysis】

This is the 18th talk of Wednesday Online Seminar on Geometric Analysis, which is an online seminar organized by Prof. Gang Tian, Prof. Jie Qing, Prof. Zhenlei Zhang, and Prof. Xiaohua Zhu.

Below is a list of invited speakers:

April 8, 2020               Wenshuai Jiang (Zhejiang University)

April 15, 2020             Chi Li (Purdue University)

April 22, 2020             Lu Wang (Caltech)

April 29, 2020             Jianchun Chu (Northwestern University)

May 6, 2020                Richard Bamler (UC Berkeley)

May 13, 2020              Xin Zhou (UC Santa Barbara)

May 20, 2020              Daniel Stern (University of Toronto)

May 27, 2020              Jeff Streets (UC Irvine)

June 3, 2020               Chenyang Xu (MIT)

June 10, 2020             Yi Lai (UC Berkeley)

June 17, 2020             Ben Andrews (Australian National University)

June 24, 2020             Shiguang Ma (Nankai University) 

July 1, 2020                Yuchen Liu (Yale University)

July 7, 2020                Min-Chun Hong (The University of Queensland)

July 15, 2020              Jian Song (Rutgers University)

September 8, 2020     Martin Kerin (NUI Galway)

September 23, 2020   Richard Bamler (UC Berkeley) 

October 14, 2020       Chao Li (Princeton University)

October 21, 2020        Yu Yuan (University of Washington)