Energy identity of harmonic map flows from surfaces at finite singular time
type: Item
instance of: scholarly article
title: Energy identity of harmonic map flows from surfaces at finite singular time
zbMATH Open document ID: 0908.58008
author: Changyou Wang
author: Fanghua Lin
published in: Calculus of Variations and Partial Differential Equations
publication date: 1999-03-18T00:00:00Z
review text: The understanding of the behavior of harmonic maps from compact Riemannian surfaces \((M,g)\) to Riemannian submanifolds \((N,h) \subset \mathbb{R}^n\) near a singular point \(T_0\) of finite time is a difficult open problem. In this framework, the authors give a different (simpler) proof of a theorem of Qing-Tian [\textit{J. Qing} and \textit{G. Tian}, Commun. Pure Appl. Math. 50, No. 4, 295-310 (1997; Zbl 0879.58017)]. Namely, they provide an energy identity for the harmonic flow \(u(\cdot,t)\), which involves a finite number of nonconstant harmonic maps \(\omega_i: S^2 \to N\) (referred to as bubbles) associated with \(u(\cdot,t)\).
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1160794
zbMATH Keywords: harmonic map flow
zbMATH Keywords: finite singular time
zbMATH Keywords: bubble energy
zbMATH Keywords: Palais-Smale sequence
reviewed by: Vladimir Balan
MaRDI profile type: Publication
full work available at URL: s005260050095
OpenAlex ID: W2024614658
DOI: 10.1007/S005260050095
description: scientific article; zbMATH DE number 1160794