Convex hull properties of harmonic maps
type: Item
instance of: scholarly article
title: Convex hull properties of harmonic maps
zbMATH Open document ID: 0926.58011
author: Peter Li
author: Jiaping Wang
published in: Journal of Differential Geometry
publication date: 1999-11-21T00:00:00Z
review text: In [Proc. Symp. Pure Math. 36, 147-151 (1980; Zbl 0455.58009)], \textit{S.-Y. Cheng} generalized the gradient estimate to harmonic maps from a manifold \(M\) with non-negative Ricci curvature to a Cartan-Hadamard manifold \(N\). In this case, the space of bounded harmonic functions \({\mathcal H}_0(M)\) is \(1\)-dimensional. The purpose of this paper is to study the image sets of harmonic maps \(u:M \to N\) from a manifold \(M\), whose space of bounded harmonic functions \({\mathcal H}_0(M)\) is finite dimensional, into a Cartan-Hadamard manifold \(N\). In fact, the manifolds \(M\) satisfying a mean value inequality \((\mathcal M)\) and a weak volume growth property \((\mathcal V)\) will have \(\dim{\mathcal H}_0(M)<{\infty}\) (see Section 3 for definitions).
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C43
zbMATH DE Number: 1268527
zbMATH Keywords: harmonic map
zbMATH Keywords: convex hull
zbMATH Keywords: Cartan-Hadamard manifold
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214460861
OpenAlex ID: W2170494849
Wikidata QID: Q115174687
DOI: 10.4310/JDG/1214460861
description: scientific article; zbMATH DE number 1268527