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Stability of harmonic maps and eigenvalues of the Laplacian


Author: Hajime Urakawa
Journal: Trans. Amer. Math. Soc. 301 (1987), 557-589
MSC: Primary 58E20; Secondary 58E05, 58G11, 58G25
DOI: https://doi.org/10.1090/S0002-9947-1987-0882704-8
MathSciNet review: 882704
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Abstract: The index and nullity of the Hessian of the energy for every harmonic map are estimated above by a geometric quantity. The stability theory of harmonic maps is developed and as an application, the Kähler version of the Lichnerowicz-Obata theorem about the first eigenvalue of the Laplacian is proved.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0882704-8
Article copyright: © Copyright 1987 American Mathematical Society

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