Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifolds
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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.References
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Additional Information
- Paul M. N. Feehan
- Affiliation: Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
- MR Author ID: 602267
- Email: feehan@math.rutgers.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3179-3190
- MSC (2010): Primary 58E20; Secondary 37D15
- DOI: https://doi.org/10.1090/proc/14013
- MathSciNet review: 3787376