Volume-preserving flow by powers of the m-th mean curvature
Differential Geometry
2009-02-13 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0902.2090,
title = {Volume-preserving flow by powers of the m-th mean curvature},
author = {Esther Cabezas-Rivas and Carlo Sinestrari},
journal= {arXiv preprint arXiv:0902.2090},
year = {2009}
}