Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
type: Item
instance of: scholarly article
title: Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature
zbMATH Open document ID: 0871.53032
DOI: 10.1007/BF01902216
author: Jeff Cheeger
author: Tobias Holck Colding
author: William P. II Minicozzi
published in: Geometric and Functional Analysis. GAFA
publication date: 1996-07-08T00:00:00Z
full work available at URL: https://eudml.org/doc/58214
review text: The main result of this paper is that for a complete Riemannian manifold \(M^n\) with nonnegative Ricci curvature any tangent cone at infinity, \(M_\infty\), splits isometrically as \(\underline{M}_\infty\times \mathbb{R}^k\), where \(\mathbb{R}^k\) has its standard flat metric, provided that the space of linear growth harmonic functions has dimension \(k+1\). A consequence of the theorem is that \(M^n\) is isometric to \(\mathbb{R}^n\) if the space of linear growth harmonic functions has dimension \(n+1\).
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 881241
zbMATH Keywords: complete Riemannian manifold
zbMATH Keywords: nonnegative Ricci curvature
zbMATH Keywords: linear growth harmonic functions
Wikidata QID: Q102415653
MaRDI profile type: Publication
cites work: Lower bounds on Ricci curvature and the almost rigidity of warped products
cites work: On the structure of spaces with Ricci curvature bounded below. III
cites work: The splitting theorem for manifolds of nonnegative Ricci curvature
cites work: Shape of manifolds with positive Ricci curvature
cites work: Large manifolds with positive Ricci curvature
cites work: Q4248253
cites work: Differential equations on riemannian manifolds and their geometric applications
cites work: Q3137120
cites work: Growth of equivariant harmonic maps and harmonic morphisms
cites work: Large time behavior of the heat equation on complete manifolds with non- negative Ricci curvature
cites work: Harmonic functions of linear growth on Kähler manifolds with nonnegative Ricci curvature
cites work: Q3137123
cites work: Linear growth harmonic functions on a complete manifold
cites work: On the parabolic kernel of the Schrödinger operator
cites work: Q4838145
cites work: Linear growth harmonic functions on complete manifolds
cites work: Q4102442
OpenAlex ID: W1975021249
Recommended article: Q3806312
Recommended article: Harmonic functions on manifolds with nonnegative Ricci curvature and linear volume growth
Recommended article: Harmonic functions of linear growth on Kähler manifolds with nonnegative Ricci curvature
Recommended article: Linear growth harmonic functions on complete manifolds
Recommended article: Linear growth harmonic functions on a complete manifold
Recommended article: Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature
Recommended article: Q4735393
Recommended article: Q3976711
Recommended article: Harmonic functions on manifolds on nonnegative Ricci curvature
Recommended article: Harmonic functions of polynomial growth on singular spaces with nonnegative Ricci curvature
description: scientific article; zbMATH DE number 881241