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The Ricci flow on the sphere with marked points

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

May 04, 2016 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Jian Song (Rutgers University)
Location: MSRI: Simons Auditorium
Tags/Keywords

  • Riemannian geometry

  • complex geometry

  • geometric analysis

  • geometric flow

  • Ricci flow

  • Ricci curvature

  • stability of solutions

  • singularities of flows

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

14503
Abstract

We study the limiting behavior of the Ricci flow on the 2-sphere with marked points. We show that the normalized Ricci flow will always converge to a unique constant curvature metric or a shrinking gradient soliton metric. In the semi-stable and unstable cases of the 2-sphere with more than two marked points, the limiting metric space carries a different conical and the complex structure from the initial structure. We also study the blow-up behavior of the flow in the semi-stable and unstable cases. This is a joint work with Phong, Sturm and Wang
Supplements
25959?type=thumb Song.Notes 1.85 MB application/pdf Download
Video/Audio Files

14503

H.264 Video 14503.mp4 330 MB video/mp4 rtsp://videos.msri.org/data/000/025/808/original/14503.mp4 Download
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