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

Esther Cabezas-Rivas; Carlo Sinestrari

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arXiv · 0902.2090

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

Esther Cabezas-Rivas·Carlo Sinestrari

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Abstract

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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Esther Cabezas-Rivas, Carlo Sinestrari. 2009-02-12. Volume-preserving flow by powers of the m-th mean curvature. https://arxiv.org/abs/0902.2090

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