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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An approach to the regularity for stable-stationary harmonic maps
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by Hsu Deliang PDF
Proc. Amer. Math. Soc. 133 (2005), 2805-2812 Request permission

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
  • Email: dlxu@sjtu.edu.cn
  • 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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2805-2812
  • MSC (2000): Primary 58E20
  • DOI: https://doi.org/10.1090/S0002-9939-05-07818-4
  • MathSciNet review: 2146230