Comparison Theorems in Riemannian Geometry
The course will cover various comparison theorems under different curvature conditions in Riemannian geometry.
Lecturer
Date
19th September ~ 14th December, 2022
Website
Prerequisite
Multivariable Calculus, Ordinary Differential Equation, Basics of Riemannian Geometry (optional)
Syllabus
1. Basics of Riemannian manifolds (quick review)
2. Jacobi fields
3. Sectional curvature comparison
4. Ricci curvature comparison
5. Selected topics
2. Jacobi fields
3. Sectional curvature comparison
4. Ricci curvature comparison
5. Selected topics
Reference
1. Riemannian Geometry - Peter Petersen
2. Comparison Theorems in Riemannian Geometry - Jeff Cheeger, D. G. Ebin
2. Comparison Theorems in Riemannian Geometry - Jeff Cheeger, D. G. Ebin
Audience
Graduate
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Dr. Pengyu Le graduated from ETH Zürich in 2018, then became a Van Loo postdoctoral fellow in University of Michigan. He joined BIMSA as an assistant professor in 2021. His research interest lies in differential geometry and general relativity.