An Isoperimetric Comparison Technique For Ricci Flow On Surfaces
Speaker(s): Dr. Paul Bryan(The Australian National University)
Time: 00:00-00:00 August 25, 2011
Venue: Room 1328 at BICMR, Resource Plaza, Peking University
Title: An Isoperimetric Comparison Technique For Ricci Flow On Surfaces
Speaker: Dr. Paul Bryan(The Australian National University)
Time: Aug 25, Thursday, 2011,14:00-16:00pm
Venue: Room 1328 at BICMR, Resource Plaza, Peking University
Abstract: I will describe a comparison principle for the evolution under the normalised Ricci flow of the isoperimetric profile on a closed surface. This may be used to obtain an exponentially decaying curvature bound, leading directly to a proof that the normalised Ricci flow on surfaces evolves any initial metric to a metric of constant curvature. This avoids any Harnack estimates and classification of singularities. Time permitting, I will indicate how the same technique may be used to obtain a curvature bound for the curve shortening flow in the plane. This is joint work with Ben Andrews.