Self-Similar Solutions to Curvature Flow of Convex Hypersurfaces
  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 $\R^{n+1}$. 
Guanghan Li, Isabel Salavessa, Chuanxi Wu