Note: The lecture on Oct. 1 will be moved to Sept. 29, B626. The lecture on Oct. 3 will be cancelled.

Description:

This course will explore various comparison theorems, such as the Rauch and Toponogov comparisons, along with their applications. Topics include the Bishop-Gromov volume comparison, sphere theorems, manifold with negative and nonnegative curvature, Gromoll-Meyer splitting theorem, and Cheeger-Gromoll soul theorem.

Prerequisite:

Differential Geometry I，Differential Geometry II

Reference:

1. Comparison Theorems in Riemannian Geometry by Jeff Cheeger, David G. Ebin (available at https://www.ams.org/books/chel/365/chel365-endmatter.pdf)

2. An invitation to Alexandrov geometry: CAT(0) spaces by Stephanie Alexander, Vitali Kapovitch and Anton Petrunin; (available at https://anton-petrunin.github.io/invitation/)

Target Audience: Undergraduate students, Graduate students

Teaching Language: English

Registration: https://www.wjx.top/vm/r5vwX0g.aspx#