On the Harnack inequality for harmonic functions on complete Riemannian manifolds
type: Item
instance of: scholarly article
title: On the Harnack inequality for harmonic functions on complete Riemannian manifolds
zbMATH Open document ID: 0782.53033
author: Jiayu Li
published in: Chinese Annals of Mathematics. Series B
publication date: 1994-03-16T00:00:00Z
review text: Let \(\overline M\) be a complete Riemannian manifold of dimension \(n\) with nonnegative Ricci curvature and \(M\) a complete Riemannian manifold uniformly equivalent to \(\overline M\). Suppose \(\text{Vol}(B_ x(r))\geq C_ n r^ n\), where \(B_ x(r)= \{y\in M\mid\text{dist}(y,x)\leq r\}\) and \(\text{Vol}(B_ x(r))\) the volume of \(B_ x(r)\). The author proves the Harnack inequality for harmonic functions on \(M\) and, as its applications, the Liouville theorem for harmonic functions and harmonic maps from \(M\).
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 205743
zbMATH Keywords: Liouville theorem
zbMATH Keywords: harmonic maps
reviewed by: Yanglian Pan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 205743