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A characterization of the $ 2$-sphere by eigenfunctions


Author: Shiu Yuen Cheng
Journal: Proc. Amer. Math. Soc. 55 (1976), 379-381
MSC: Primary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1976-0405296-4
MathSciNet review: 0405296
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Abstract: The spheres in $ 3{\text{ - dim}}$ Euclidean space are characterized by the fact that they have three 1st eigenfunctions with square sum equal to a constant.


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  • [1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., vol. 194, Springer-Verlag, Berlin and New York, 1971. MR 43 #8025. MR 0282313 (43:8025)
  • [2] S. Y. Cheng, Nodal sets and eigenfunctions, Comment. Math. Helv. (to appear). MR 0397805 (53:1661)
  • [3] J. Hersch, Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1645-A1648. MR 45 #1444. MR 0292357 (45:1444)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0405296-4
Keywords: Eigenfunctions, eigenvalues
Article copyright: © Copyright 1976 American Mathematical Society

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