Harmonic maps and a pinching theorem for positively curved hypersurfaces

Hu, H. S.; Pan, Y. L.; Shen, Y. B.

doi:10.1090/S0002-9939-1987-0866450-8

Harmonic maps and a pinching theorem for positively curved hypersurfaces
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by H. S. Hu, Y. L. Pan and Y. B. Shen

Proc. Amer. Math. Soc. 99 (1987), 182-186

DOI: https://doi.org/10.1090/S0002-9939-1987-0866450-8

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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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