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Proceedings of the American Mathematical Society

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Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifolds

Author: Paul M. N. Feehan
Journal: Proc. Amer. Math. Soc. 146 (2018), 3179-3190
MSC (2010): Primary 58E20; Secondary 37D15
Published electronically: March 19, 2018
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Abstract: We extend the well-known Sacks-Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.

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Paul M. N. Feehan
Affiliation: Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

Keywords: Harmonic maps, {\L}ojasiewicz--Simon gradient inequality
Received by editor(s): September 12, 2017
Published electronically: March 19, 2018
Additional Notes: The author was partially supported by National Science Foundation grant DMS-1510064 and the Oswald Veblen Fund and Fund for Mathematics (Institute for Advanced Study, Princeton) during the preparation of this article.
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society

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