General Sobolev Inequality on Riemannian Manifold
Qihua Ruan, Zhihua Chen
Abstract
Let M be a complete n-dimensional Riemannian manifold, if the sobolev inqualities hold on M, then the geodesic ball has maximal volume growth; if the Ricci curvature of M is nonnegative, and one of the general Sobolev inequalities holds on M, then M is diffeomorphic to Rn.
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