Manifolds with non-negative Ricci curvature and Nash inequalities

2004/08/30 by Qihua Ruan, Zhihua Chen, Ruan, Qihua +1
Mathematics · Physics and Astronomy · #53C23 #Advanced Differential Geometry Research #Algebraic Topology (math.AT) #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Inequality #Mathematical analysis #Mathematical economics #Mathematics #Primary 53C20 #Pure mathematics #Ricci curvature #Secondary 58B05 #math.AT #math.DG #msc:53C20 #msc:53C23 #msc:58B05

paper · pdf · doi:10.48550/arxiv.math/0408422

five pages, latex file

arxiv created 2004/08/30 · openalex publication_date 2004/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied, then it is diffeomorphic to Rⁿl.

Citations

• Ricci flow and the uniformization on complete noncompact Kähler manifolds
• Geometry of Manifolds
• Heat Kernels and Spectral Theory

Related

• General Sobolev Inequality on Riemannian Manifold
• Sobolev inequalities on manifolds with nonnegative Bakry-Émery Ricci curvature
• Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature
• Hardy type inequalities on manifolds with nonnegative Ricci curvature
• Remark on an inequality for closed hypersurfaces in complete manifolds with nonnegative Ricci curvature