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.