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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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  • [1] S. S. Chern and S. I. Goldberg, On the volume decreasing property of a class of real harmonic mappings, Amer. J. Math. 97 (1975), 133-147. MR 0367860 (51:4102)
  • [2] J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68. MR 495450 (82b:58033)
  • [3] P. F. Leung, On the stability of harmonic maps, Lecture Notes in Math., vol. 949, Springer-Verlag, pp. 122-129. MR 673586 (83m:58033)
  • [4] Y. L. Pan and Y. B. Shen, Stability of harmonic maps and minimal immersions, Proc. Amer. Math. Soc. 93 (1985), 111-117. MR 766539 (86f:58038)
  • [5] Y. L. Xin, Topology of certain submanifolds in the Euclidean sphere, Proc. Amer. Math. Soc. 82 (1981), 643-648. MR 614895 (82e:58036)
  • [6] -, Some results on stable harmonic maps, Duke Math. J. 47 (1980), 609-613. MR 587168 (81j:58041)

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

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