Volume-preserving flow by powers of the m-th mean curvature

Details Volume-preserving flow by powers of the m-th mean curvature Volume-preserving flow by powers of the m-th mean curvature

2009-02-12

arxiv.org/abs/0902.2090v1

Mathematics

Differential Geometry

Scientific paper

We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the m-th mean curvature plus a volume preserving term, including the case of powers of the mean curvature or of the Gauss curvature. We prove that if the initial hypersurface satisfies a suitable pinching condition, the solution exists for all times and converges to a round sphere.

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