Volume-preserving flow by powers of the mth mean curvature |
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Authors: | Esther Cabezas-Rivas Carlo Sinestrari |
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Institution: | 1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK 2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy
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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 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. |
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