On the singular set of stationary harmonic maps
type: Item
instance of: scholarly article
title: On the singular set of stationary harmonic maps
zbMATH Open document ID: 0792.53039
DOI: 10.1007/BF02599324
author: Fabrice Béthuel
published in: Manuscripta Mathematica
publication date: 1994-08-02T00:00:00Z
full work available at URL: https://eudml.org/doc/155819
review text: Thm. If \(n: M \to N\) is a stationary harmonic map between compact Riemannian manifolds, then its singular set has Hausdorff \((n-2)\)- dimensional measure, \(n = \dim M\). This was proved by [\textit{L. C. Evans}, Arch. Ration. Mech. Anal. 116, No. 2, 101-113 (1991; Zbl 0754.58007)] when \(N =S^ m\). Extending results of [\textit{F. Hélein}, Manuscr. Math. 70, No. 2, 203-218 (1991; Zbl 0718.58019)] the author proves the Theorem: If \(u\) is a weakly harmonic map in \(W^{1,n}(M,N)\), then \(u\) is smooth. The author's methods rely strongly on those of these two papers.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 492742
zbMATH Keywords: singular set
zbMATH Keywords: weakly harmonic map
reviewed by: J. Eells
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492742