General Sobolev Inequality on Riemannian Manifold

Qihua Ruan; Zhihua Chen

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General Sobolev Inequality on Riemannian Manifold

Qihua Ruan·Zhihua Chen

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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 $R^{n}$.

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Qihua Ruan, Zhihua Chen. 2005-01-01. General Sobolev Inequality on Riemannian Manifold. https://arxiv.org/abs/math/0501009

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