Hermitian harmonic maps from complete Hermitian manifolds to complete Riemannian manifolds
type: Item
instance of: scholarly article
title: Hermitian harmonic maps from complete Hermitian manifolds to complete Riemannian manifolds
zbMATH Open document ID: 0944.58013
author: Lei Ni
published in: Mathematische Zeitschrift
publication date: 2000-09-11T00:00:00Z
review text: In Acta Math. 170, No. 2, 221-254 (1993; Zbl 0806.53064), \textit{J. Jost} and \textit{S.-T. Yau} introduced a nonlinear elliptic system (H) for maps from a Hermitian manifold \(M\) to a Riemannian manifold \(N\). The solutions of (H) are called Hermitian harmonic maps. When \(M\) is not Kähler, then holomorphic maps are not necessarily harmonic, but always Hermitian harmonic. Jost and Yau also gave an existence and uniqueness theorem for Hermitian harmonic maps homotopic to a given \(h: M\to N\) relative to \(\partial M\), when \(N\) is nonpositively curved. In the present paper, the results of Jost and Yau are generalized to the case where \(M\) is no longer compact but complete. Here, compactness of \(M\) is replaced by positivity of the first eigenvalue of the Laplacian associated to a fixed holomorphic torsion-free connection and certain \(L^p\) bounds on the given data. The author also gives conditions for the global existence of the Hermitian harmonic map heat flow associated to (H) and starting from \(h\). Under certain additional assumptions, this heat flow converges to a Hermitian harmonic map.
reviewed by: Sebastian Goette
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 1384392
zbMATH Keywords: Hermitian harmonic map heat flow
MaRDI profile type: Publication
full work available at URL: s002090050518
OpenAlex ID: W2006694220
Wikidata QID: Q115388841
DOI: 10.1007/S002090050518
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description: scientific article; zbMATH DE number 1384392