General Sobolev Inequality on Riemannian Manifold
Differential Geometry
2007-05-23 v1 Geometric Topology
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 .
Cite
@article{arxiv.math/0501009,
title = {General Sobolev Inequality on Riemannian Manifold},
author = {Qihua Ruan and Zhihua Chen},
journal= {arXiv preprint arXiv:math/0501009},
year = {2007}
}
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4 pages