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On the singular set of stationary harmonic maps

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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]).

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Authors and Affiliations

  1. Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan et CNRS, 61 Avenue du Président Wilson, 94235, Cachan Cedex, France

    Fabrice Bethuel

  2. Cerma-ENPC, La Courtine, 93167, Noisy Le Grand Cedex, France

    Fabrice Bethuel

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  1. Fabrice Bethuel
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Bethuel, F. On the singular set of stationary harmonic maps. Manuscripta Math 78, 417–443 (1993). https://doi.org/10.1007/BF02599324

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