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Comparison geometry for Ricci curvature I

Introductory Workshop: Modern Riemannian Geometry January 18, 2016 - January 22, 2016

January 18, 2016 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Guofang Wei (University of California, Santa Barbara)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • differential geometry

  • Riemannian geometry

  • modern geometry

  • curvature

  • curvature estimates

  • Ricci curvature

  • Ricci curvature lower bounds

  • Bishop-Gromov volume

  • heat kernel eigenvalues

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14422

Abstract

Ricci curvature occurs in the Einstein equation, Ricci flow, optimal transport, and is important both in mathematics and physics. Comparison method is one of the key tools in studying the Ricci curvature. We will start with Bochner formula and derive Laplacian comparison, Bishop-Gromov volume comparison, first eigenvalue and heat kernel comparison and some application. Then we will discuss some of its generalizations to Bakry-Emery  Ricci curvature and integral Ricci curvature

Supplements
25662?type=thumb Wei Notes 504 KB application/pdf Download
Video/Audio Files

14422

H.264 Video 14422.mp4 284 MB video/mp4 rtsp://videos.msri.org/data/000/025/260/original/14422.mp4 Download
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