Manifold with nonnegatively pinched curvature

Lee, Man-Chun 李文俊

The Chinese University of Hong Kong

Man-Chun Lee is an Assistant Professor at the Chinese University of Hong Kong (CUHK). He received his PhD in mathematics from CUHK in 2018. In 2019-2021, he worked as a Boas Assistant Professor at Northwestern University and research fellow at Warwick University. He came back to Hong Kong and joined CUHK in 2021. His research interests center around Geometric Analysis, Geometric Partial Differential Equations, and Complex Geometry.

# Time

Monday, 14:00-15:00

Oct. 21, 2024

# Venue

Lecture Hall C548

Shuangqing Complex Building A

清华大学双清综合楼A座C548报告厅

#Abstract

On compact manifold, differentiable sphere theorem infers that manifold with 1/4 pinched positive curvature are necessarily sphere. Using Ricci flow method, it was shown by Brendle-Schoen that indeed the sphere theorem holds under an even weaker pinched 1-isotropic curvature condition. Motivated by this, It was conjectured by Hamilton-Lott that the in three manifold, noncompact manifold with pinched nonnegative Ricci (equivalent to 1-isotropic curvature) is necessarily flat. In this talk, we will discuss some recent advances in three dimensions and its generalization in higher dimension. This is based on joint work with P. Topping.