Bubbling analysis for approximate Lorentzian harmonic maps from Riemann surfaces
type: Item
instance of: scholarly article
title: Bubbling analysis for approximate Lorentzian harmonic maps from Riemann surfaces
zbMATH Open document ID: 1384.53058
author: Peng Zhang
published in: Calculus of Variations and Partial Differential Equations
publication date: 2018-01-11T00:00:00Z
review text: This paper focusses on the study of harmonic maps from a Riemann surface \(M\) into a Lorentzian manifold \(N\times\mathbb{R}\) that is equipped with a warped product metric of the form \(g=g_N-\beta(d\theta+\omega)^2\), where \((N,g_N)\) is a compact Riemannian manifold, \((\mathbb{R},d\theta^2)\) is the 1-dimensional Euclidean space, \(\beta\) is a positive \(C^\infty\) function on \(N\) and \(\omega\) is a smooth 1-form on \(N\). In the main results of the article, the authors prove some energy identities of an approximate Lorentzian harmonic map sequence and get the no-neck property during a blow-up process, provided that \(M\) is a compact Riemann surface with boundary.
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 6824820
zbMATH Keywords: harmonic map
zbMATH Keywords: Riemannian surface
zbMATH Keywords: Lorentzian manifold
zbMATH Keywords: energy identity
Wikidata QID: Q59527498
reviewed by: Gabriel Eduard Vilcu
MaRDI profile type: Publication
full work available at URL: s00526-017-1271-0
OpenAlex ID: W2613160117
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DOI: 10.1007/S00526-017-1271-0
description: scientific article; zbMATH DE number 6824820