Surfaces moving by powers of Gauss curvature
Differential Geometry
2011-11-22 v1 Analysis of PDEs
Abstract
We prove that strictly convex surfaces moving by become spherical as they contract to points, provided lies in the range . In the process we provide a natural candidate for a curvature pinching quantity for surfaces moving by arbitrary functions of curvature, by finding a quantity conserved by the reaction terms in the evolution of curvature.
Cite
@article{arxiv.1111.4616,
title = {Surfaces moving by powers of Gauss curvature},
author = {Ben Andrews and Xuzhong Chen},
journal= {arXiv preprint arXiv:1111.4616},
year = {2011}
}