Talk
Comparison geometry and Ricci curvature
- Bobo Hua
Abstract
In this course, we shall study some basic facts about manifolds with lower Ricci (sectional) curvature bound in the comparison geometry such as Cheng-Myers' theorem, Bishop-Gromov volume comparison, the Laplacian comparison and Cheeger-Gromoll's splitting theorem. Topological obstructions of manifolds with nonnegative Ricci curvature will be investigated. To understand the structure theory of the limit space of a sequence of manifolds with Ricci curvature bounded below (by Cheeger-Colding) is our main purpose. In the end, we survey the harmonic function theory on manifolds with nonnegative Ricci curvature (Cheng-Yau, Colding-Minicozzi, Li).
Date and time info
Monday, 13:30 - 15:00 h
