Paul Allen : The Dirichlet problem for curve shortening flow.
We consider the Dirichlet problem for curve shortening flow on surfaces of constant curvature and show long-time existence of the flow when the initial curve is embedded in a convex region. Furthermore, the limit curve of the flow is a geodesic. The proof relies on an adaptation of Huisken's distance comparison estimate for planar curves, a maximum principle of Angenent, and a blow-up analysis of singularities.
- Category: Geometry and Topology
- Duration: 01:14:53
- Date: October 29, 2012 at 4:25 PM
- Tags: seminar, Geometry/topology Seminar