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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Keywords: Harmonic map, hypersurface, stable, pinching theorem
Article copyright: © Copyright 1987 American Mathematical Society