Stability of harmonic maps and minimal immersions

Pan, Y. L.; Shen, Y. B.

doi:10.1090/S0002-9939-1985-0766539-6

Stability of harmonic maps and minimal immersions
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by Y. L. Pan and Y. B. Shen PDF

Proc. Amer. Math. Soc. 93 (1985), 111-117 Request permission

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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