Monotone Quantities and Unique Limits for Evolving Convex Hypersurfaces
نویسنده
چکیده
The aim of this paper is to introduce a new family of monotone integral quantities associated with certain parabolic evolution equations for hypersurfaces, and to deduce from these some results about the limiting behaviour of the evolving hypersurfaces. A variety of parabolic equations for hypersurfaces have been considered. One of the earliest was the Gauss curvature flow, introduced in [Fi] as a model for the changing shape of a stone wearing on a beach. The stone is represented by a bounded convex region, and each point on its surface moves in the inward normal direction with speed equal to the Gauss curvature: If the surface at time t is given by an embedding xt, then
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