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Comparison geometry for Ricci curvature II

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

January 20, 2016 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Guofang Wei (University of California, Santa Barbara)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • differential geometry

  • modern geometry

  • curvature

  • Riemannian geometry

  • 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

14430
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
25668?type=thumb Wei Notes 5.32 MB application/pdf Download
Video/Audio Files

14430

H.264 Video 14430.mp4 340 MB video/mp4 rtsp://videos.msri.org/14430/14430.mp4 Download
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