Event
Mohammad Najafi, T.U. Wien and Concordia
Friday, February 17, 2017 13:30to14:00
Room LB-921-04, Library Building Concordia, 1400 de Maisonneuve West, Montreal, QC, H3G 1M8, CA
On the classification of ancient solutions to curvature flows on the sphere.聽
An ancient solution to a curvature flow is a solution that exists backwards in time forever. In this talk, I will discuss the classification of ancient solutions to curvature flows on the sphere. I will prove that the sphere exhibits a very strong rigidity: any ancient solution of a curvature flow which satisfies a backwards in time uniform bound on mean curvature must be stationary or a family of shrinking geodesic sphere. The main tools are geometric, employing the maximum principle, a rigidity result in the sphere and an Alexandrov reflection argument.