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An approach to the regularity for stable-stationary harmonic maps

Author: Hsu Deliang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2805-2812
MSC (2000): Primary 58E20
Published electronically: March 22, 2005
MathSciNet review: 2146230
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Abstract: In this paper we investigate the regularity of stable-stationary harmonic maps. By assuming that the target manifolds do not carry any stable harmonic $S^{2}$, we obtain some compactness results and regularity theorems. In particular, we prove that the Hausdorff dimension of the singular set of these maps cannot exceed $n-3$, and the dimension estimate is optimal.

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Additional Information

Hsu Deliang
Affiliation: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China

Keywords: Stable harmonic map, stationary harmonic map, blowing-up map
Received by editor(s): December 15, 2003
Received by editor(s) in revised form: May 4, 2004
Published electronically: March 22, 2005
Additional Notes: The author was supported in part by Chinese NSF Grant 10301020.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.