Volume-preserving flow by powers of the mth mean curvature

By Esther Cabezas-Rivas, Carlo Sinestrari. 2009

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/835d1f7387ea17ceacfaa3e1775fd78604c7ddee