Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces
type: Item
instance of: scholarly article
title: Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces
zbMATH Open document ID: 1116.53037
DOI: 10.5565/PUBLMAT_50206_03
author: Qiaoling Wang
published in: Publicacions Matemàtiques
publication date: 2007-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/41591
review text: The paper identifies two more sets of geometric restrictions to a Riemannian manifold \(M^m\) which allow to prove a Liouville type theorem for harmonic maps to complete manifolds \(N^n\) of nonpositive sectional curvature. (1) Suppose \(M\) is a complete non-compact Riemannian manifold of dimension \(\geq2\). Assume that \(\lambda_1(M)>0\) and the Ricci curvature of \(M\) is bounded from below by \(-(1+{1\over2mn})\lambda_1(M)+\delta\). Then any harmonic map \(M\to N\) with finite energy is constant. (2) The same conclusion holds if \(M\) is a complete oriented noncompact stable minimal hypersurface in a complete Riemannian manifold of non-negative bi-Ricci curvature. The ususal topological consequences of such Liouville theorems hold.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5140580
zbMATH Keywords: Liouville theorems
zbMATH Keywords: harmonic maps
zbMATH Keywords: topology
zbMATH Keywords: manifolds
zbMATH Keywords: spectrum
zbMATH Keywords: minimal hypersurfaces
MaRDI profile type: Publication
Recommended article: Harmonic maps, harmonic morphisms and stability
Recommended article: Q4827152
Recommended article: Q4650721
Recommended article: Q3831753
Recommended article: Q4358922
Recommended article: Regularity of harmonic maps into positively curved manifolds
Recommended article: Q3768040
Recommended article: Harmonic maps and $s$-regular manifolds
Recommended article: The spectral geometry of harmonic maps into \(HP^n(c)\)
Recommended article: Q3198564
description: scientific article; zbMATH DE number 5140580