Volume-preserving flow by powers of the mth mean curvature
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- Cabezas-Rivas, E. & Sinestrari, C. Calc. Var. (2010) 38: 441. doi:10.1007/s00526-009-0294-6
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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 mth 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.