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Proceedings of the American Mathematical Society

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Removability of the singular set
of the heat flow of harmonic maps


Authors: Yunmei Chen and Livio Flaminio
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
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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

DOI: https://doi.org/10.1090/S0002-9939-96-03169-3
Keywords: Heat flow, harmonic maps
Received by editor(s): September 4, 1994
Additional Notes: The first author was supported by NSF grant #DMS-9101911
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society