English

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 Kα/2K^{\alpha/2} become spherical as they contract to points, provided α\alpha lies in the range [1,2][1,2]. 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.

Keywords

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}
}