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Energy identity for approximations of harmonic maps from surfaces


Author: Tobias Lamm
Journal: Trans. Amer. Math. Soc. 362 (2010), 4077-4097
MSC (2010): Primary 58E20; Secondary 35J60, 53C43
DOI: https://doi.org/10.1090/S0002-9947-10-04912-3
Published electronically: March 23, 2010
MathSciNet review: 2608396
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two approximations and on estimates for the concentration radius of bubbles.


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Additional Information

Tobias Lamm
Affiliation: Max-Planck-Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Golm, Germany
Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada V6T 1Z2
Email: tlamm@math.ubc.ca

DOI: https://doi.org/10.1090/S0002-9947-10-04912-3
Keywords: Geometric analysis, harmonic maps, energy identity
Received by editor(s): December 17, 2007
Published electronically: March 23, 2010
Additional Notes: The author would like to thank Yuxiang Li for pointing out an error in an earlier version of the paper.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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