Bubble tree for approximate harmonic maps
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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
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 2849-2857
- MSC (2010): Primary 53C43, 58E20
- DOI: https://doi.org/10.1090/S0002-9939-2014-11964-2
- MathSciNet review: 3209338