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.
Cabezas Rivas, E., Sinestrari, C. (2010). Volume-preserving flow by powers of the m-th mean curvature. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 38, 441-469 [10.1007/s00526-009-0294-6].
Volume-preserving flow by powers of the m-th mean curvature
SINESTRARI, CARLO
2010-01-01
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.File in questo prodotto:
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