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Global solutions of the Teichmueller harmonic map flow

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

May 06, 2016 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Peter Topping (University of Warwick)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • harmonic maps

  • Riemannian geometry

  • complex geometry

  • geometric analysis

  • geometric flow

  • Ricci flow

  • diffeomorphism groups

  • singularities of flows

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

14508

Abstract

The Teichmueller harmonic map flow is a gradient flow of the classical harmonic map energy, in which both a map from a surface and the metric on that surface are allowed to evolve. In principle, the flow wants to find minimal immersions. However, in general, the domain metric might degenerate in finite time. In this talk we show how to flow beyond finite time singularities, and this allows us to decompose a general map into a collection of minimal immersions.

This is forthcoming work joint with Melanie Rupflin

Supplements
25965?type=thumb Topping.Notes 3.15 MB application/pdf Download
Video/Audio Files

14508

H.264 Video 14508.mp4 320 MB video/mp4 rtsp://videos.msri.org/data/000/025/818/original/14508.mp4 Download
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