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

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Cabezas-Rivas, Esther
Sinestrari, Carlo
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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.
Keywords
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, 53C44
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