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Convergence of Ricci flows with bounded scalar curvature

Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016

May 05, 2016 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Richard Bamler (University of California, Berkeley)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • complex geometry

  • Riemannian geometry

  • geometric analysis

  • geometric flow

  • curvature estimates

  • Ricci curvature

  • Ricci flow

  • singularities of flows

  • bounded curvature

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

14505
Abstract

It is a basic fact that the Riemannian curvature becomes unbounded at every finite-time singularity of the Ricci flow. Sesum showed that the same is true for the Ricci curvature. It has since remained a conjecture whether also the scalar curvature becomes unbounded at any singular time.

In this talk I will show that, given a uniform scalar curvature bound, the Ricci flow can only degenerate on a set of codimension bigger or equal to 4, if at all. This result is a consequence of a structure theory for such Ricci flows, which relies on and generalizes recent work of Cheeger and Naber
Supplements
25963?type=thumb Bamler.Notes 1.52 MB application/pdf Download
Video/Audio Files

14505

H.264 Video 14505.mp4 330 MB video/mp4 rtsp://videos.msri.org/14505/14505.mp4 Download
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