General Sobolev Inequality on Riemannian Manifold

2005/01/01 by Qihua Ruan, Zhihua Chen, Ruan, Qihua +1
Mathematics · #53C20 #53C21 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Nonlinear Partial Differential Equations #math.DG #math.GT #msc:53C20 #msc:53C21

paper · pdf · doi:10.48550/arxiv.math/0501009

4 pages

arxiv created 2005/01/01 · openalex publication_date 2005/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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