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Bubble tree for approximate harmonic maps


Author: Xiangrong Zhu
Journal: Proc. Amer. Math. Soc. 142 (2014), 2849-2857
MSC (2010): Primary 53C43, 58E20
Published electronically: May 6, 2014
MathSciNet review: 3209338
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Abstract: In this paper, we set up the complete bubble tree theory for approximate harmonic maps from a Riemann surface with tension fields bounded in Zygmund class $ L\ln ^+ L$. Some special cases of this theory have previously been used in a number of papers.

On the other hand, one can see that this bubble tree theory is not true for the general target manifold if we only assume that the tension fields are bounded in $ L^1$ uniformly.


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Additional Information

Xiangrong Zhu
Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People’s Republic of China
Email: zxr701197@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11964-2
Received by editor(s): August 2, 2011
Received by editor(s) in revised form: July 14, 2012
Published electronically: May 6, 2014
Additional Notes: The author was supported by NSFC(11101372)
Communicated by: Michael Wolf
Article copyright: © Copyright 2014 American Mathematical Society