Curvature Flows with Free Boundaries
Seminar Room 2, Newton Institute Gatehouse
AbstractIn this talk, we are going to discuss alpha- Gauss Curvature Flows with free boundaries. For a=1n, a flat spot on convex manifold will persists for some time, which is similar as the waiting time in Porous Medium Equations. Naturally, the interface between strictly convex region and flat spot will form a free boundary that will moves along the time. We will show the relation between optimal regularity and bounded nondegenerate speed of free boundaries. The optimal regularity and the smoothness of the free boundary will be discussed. We will also consider the dynamics and regularity of free boundary of the manifold with a concave region.
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