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

DOI:
https://doi.org/10.1090/S0002-9939-1985-0766539-6

MathSciNet review:
766539

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Abstract | References | Similar Articles | Additional Information

Abstract: It was proved by J. Simons [**10**] that there does not exist any stable minimal submanifold in the Euclidean sphere , and P. F. Leung proved that any stable harmonic map from any Riemannian manifold to , where , is a constant. In this paper, we generalize their results and indicate that there are many manifolds having such properties as .

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0766539-6

Article copyright:
© Copyright 1985
American Mathematical Society