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manuscripta mathematica

, Volume 78, Issue 1, pp 417–443 | Cite as

On the singular set of stationary harmonic maps

  • Fabrice Bethuel
Article

Abstract

LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatH n−2 (Σ)=0, wheren=dimM and Σ is the singular set ofu. This is a generalization of a result of C. Evans [7], where this is proved in the special caseN is a sphere. We also prove that, ifu is a weakly harmonic map inW 1,n (M, N), thenu is smooth. This extends results of F. Hélein for the casen=2, or the caseN is a sphere ([9], [10]).

Keywords

Hardy Space Differential Form Absolute Constant Compact Riemannian Manifold Monotonicity Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Fabrice Bethuel
    • 1
    • 2
  1. 1.Centre de Mathématiques et de Leurs ApplicationsEcole Normale Supérieure de Cachan et CNRSCachan CedexFrance
  2. 2.Cerma-ENPCNoisy Le Grand CedexFrance

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