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Stability of harmonic maps and minimal immersions

Authors: Y. L. Pan and Y. B. Shen
Journal: Proc. Amer. Math. Soc. 93 (1985), 111-117
MSC: Primary 58E20; Secondary 53C42
MathSciNet review: 766539
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Abstract: It was proved by J. Simons [10] that there does not exist any stable minimal submanifold in the Euclidean sphere $ {S^n}$, and P. F. Leung proved that any stable harmonic map from any Riemannian manifold to $ {S^n}$, where $ n \geqslant 3$, is a constant. In this paper, we generalize their results and indicate that there are many manifolds having such properties as $ {S^n}$.

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