On manifolds with non-negative Ricci curvature and Sobolev inequalities
type: Item
instance of: scholarly article
title: On manifolds with non-negative Ricci curvature and Sobolev inequalities
zbMATH Open document ID: 0953.53025
published in: Communications in Analysis and Geometry
publication date: 2001-01-22T00:00:00Z
review text: The following result is given. A complete \(n\)-dimensional Riemann manifold \(M\) with nonnegative Ricci curvature is isometric to \(\mathbb{R}^n\) if for all \(C^{\infty}\) compactly supported functions \(f\) on \(M\) the Sobolev inequality \((\int|f|^p dv)^{1/p}\leq C(\int |\bigtriangledown f|^q dv)^{1/q} (1/q)-(1/p)=1/n\) is satisfied with ``optimal'' \(C\).
reviewed by: János Aczél
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 26E20
Mathematics Subject Classification ID: 58C35
zbMATH DE Number: 1309818
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: Riemann manifold
zbMATH Keywords: compact support
zbMATH Keywords: Ricci curvature
author: Michel Ledoux
MaRDI profile type: Publication
Wikidata QID: Q126172660
DOI: 10.4310/CAG.1999.V7.N2.A7
description: scientific article; zbMATH DE number 1309818