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Fully nonlinear flows with surgery

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

May 02, 2016 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Simon Brendle (Stanford University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • complex geometry

  • Riemannian geometry

  • geometric analysis

  • geometric flow

  • positive curvature

  • curvature flow

  • Ricci flow

  • singularities of flows

  • surgery on flows

  • hypersurfaces

  • Convex geometry

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

14494

Abstract

We will present joint work with Gerhard Huisken on a fully nonlinear flow for hypersurfaces in Riemannian manifolds. Unlike mean curvature flow, this flow preserves two-convexity in a general ambient manifold. For this fully nonlinear flow, we establish a convexity estimate, a cylindrical estimate, and a pointwise curvature derivative estimate. These estimates allow us to extend the flow beyond singularities by a surgery procedure, similar to the ones developed by Hamilton and Perelman for the Ricci flow and by Huisken and Sinestrari for mean curvature flow

Supplements
25954?type=thumb Brendle.Notes 1.35 MB application/pdf Download
Video/Audio Files

14494

H.264 Video 14494.mp4 327 MB video/mp4 rtsp://videos.msri.org/data/000/025/781/original/14494.mp4 Download
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