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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Harmonic maps and a pinching theorem for positively curved hypersurfaces


Authors: H. S. Hu, Y. L. Pan and Y. B. Shen
Journal: Proc. Amer. Math. Soc. 99 (1987), 182-186
MSC: Primary 58E20; Secondary 53C20, 53C40
MathSciNet review: 866450
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Abstract: In this paper, we establish a theorem of Liouville type for stable harmonic maps in sufficiently pinched, positively curved hypersurfaces of a space form with nonnegative constant curvature. Similar results for the Euclidean sphere $ {S^n}$ have been proved by Y. L. Xin and P. F. Leung, respectively.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866450-8
PII: S 0002-9939(1987)0866450-8
Keywords: Harmonic map, hypersurface, stable, pinching theorem
Article copyright: © Copyright 1987 American Mathematical Society