Self-Similar Solutions to Curvature Flow of Convex Hypersurfaces

Abstract

We classify the self-similar solutions to a class of Weingarten curvature flow of connected compact convex hypersurfaces, isometrically immersed into space forms with non-positive curvature, and obtain a new characterization of a sphere in a Euclidean space ${\mathbb{R}}^{n+1}$.

12 pages, Latex v2 is a largely extended new version