清华主页 EN
导航菜单

Comparison Theorems in Riemannian Geometry

来源: 09-09

时间:08:50 - 10:35, Mon,Wed, 9/19/2022 - 12/14/2022

地点:Venue: 1129B Zoom: 482 240 1589 PW: BIMSA

主讲人:Pengyu Le (Assistant Research Fellow)

Record: No

Level: Graduate

Language: Chinese


Prerequisite

Multivariable Calculus, Ordinary Differential Equation, Basics of Riemannian Geometry (optional)


Abstract

The course will cover various comparison theorems under different curvature conditions in Riemannian geometry.


Reference

1. Riemannian Geometry - Peter Petersen

2. Comparison Theorems in Riemannian Geometry - Jeff Cheeger, D. G. Ebin


Syllabus

1. Basics of Riemannian manifolds (quick review)

2. Jacobi fields

3. Sectional curvature comparison

4. Ricci curvature comparison

5. Selected topics


Lecturer Intro


Lecturer Email: pengyu.le@bimsa.cn

TA: Dr. Xuefeng Feng, fengxuefeng@bimsa.cn



返回顶部
相关文章
  • A comparison of categorical and topological entropies on Weinstein manifolds

    AbstractEvery symplectic automorphism on a symplectic manifold induces an auto-equivalence on the (derived) Fukaya category, which gives rise to a categorical dynamical system. In this talk, I will first give a brief review of various Fukaya categories of symplectic manifolds with boundaries. Then, for a given symplectic automorphism, I will discuss how the categorical entropies of auto-equival...

  • Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds

    AbstractKinetic Brownian motion is a stochastic process that interpolates between the geodesic flow and Laplacian. It is also an analogue of Bismut’s hypoelliptic Laplacian. We prove the strong convergence of the spectrum of kinetic Brownian motion to the spectrum of base Laplacian for all compact Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf on constant curvature sur...