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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 RnR^{n}.

Keywords

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}
}

Comments

4 pages

R2 v1 2026-07-22T17:14:06.304Z