Monotone quantities and unique limits for evolving convex hypersurfaces

Research Report MRR97-033

Monotone quantities and unique limits for evolving convex hypersurfaces

Ben Andrews

Abstract: We introduce a family of integral quantities associated with a class of evolution equations for convex hypersurfaces. We show monotonicity of these quantities in time, and use the results to prove that hypersurfaces evolving under these equations have well-defined limiting shapes as they contract to points.

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