SOBOLEV-TYPE INEQUALITIES AND COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

摘要

Let M be an n-dimensional complete Riemannian manifold, we investigate the geometric nature of such M which admits any of the family of Sobolev-type inequalities with the optimal Euclidean Sobolev constant. This leads to several conditions under which M with nonnegative Ricci curvature is isometric to Euclidean space R n .