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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Removability of the singular set of the heat flow of harmonic maps
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by Yunmei Chen and Livio Flaminio PDF
Proc. Amer. Math. Soc. 124 (1996), 513-525 Request permission

Abstract:

We show that the singular set of a weak stationary solution $u$ of the heat flow of harmonic maps between Riemannian manifolds $M$ and $N$, with $N$ compact, is removable if it has “parabolic codimension” greater than two and the initial energy $E(u_0)$ is sufficiently small.
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Additional Information
  • Yunmei Chen
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • Email: yunmei@math.ufl.edu
  • Livio Flaminio
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • Email: flaminio@math.ufl.edu
  • Received by editor(s): September 4, 1994
  • Additional Notes: The first author was supported by NSF grant #DMS-9101911
  • Communicated by: Peter Li
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 513-525
  • MSC (1991): Primary 35B65, 35D10, 49N60, 35Kxx, 58E20, 58G11
  • DOI: https://doi.org/10.1090/S0002-9939-96-03169-3
  • MathSciNet review: 1307502