## An approach to the regularity for stable-stationary harmonic maps

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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.## References

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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