Self-shrinkers and Translating Solitons Related to the Anisotropic Mean Curvature Flow
摘要
Our aim in this paper is investigate geometric conditions which guarantee either the umbilicity or nonexistence of self-shrinkers and translating solitons related to the anisotropic mean curvature flow in the Euclidean space. Our approach is based on three main analytical frameworks: a Liouville type result, a maximum principle for complete noncompact Riemannian manifolds with either polynomial or exponential volume growth and a suitable version of the Omori-Yau maximum principle.