Speaker: Professor Ki-Ahm Lee (Seoul National University, South Korea)
Title: Gauss Curvature flows
Time: 2009-07-10 (Fri.)  10:30 - 11:30
Abstract: In this talk, we are going to consider Gauss Curvature flows describing the wearing process of the rolling rock. The speed of erosion in the inward normal direction is proportional to the Gauss Curvature of the point on the surface. When the initial surface has a fat spot, some principle curvature will be degenerate near the interface between the flat spot and the strictly convex part. Then the fully nonlinear parabolic equation will be degenerate near the interface. We are going to show the optimal regularity of the surface across the interface and the smoothness of the strictly convex part up to the interface in weighted space. We also consider the surface with nonconvex part which makes the equations is nonlocal and discuss the regularity of the surface and the interface.  
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