A characterization of the 2-sphere by eigenfunctions

Cheng, Shiu Yuen

doi:10.1090/S0002-9939-1976-0405296-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of the $2$-sphere by eigenfunctions
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Proc. Amer. Math. Soc. 55 (1976), 379-381 Request permission

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.

References

Marcel Berger, Paul Gauduchon, and Edmond Mazet, Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York, 1971 (French). MR 0282313
Shiu Yuen Cheng, Eigenfunctions and nodal sets, Comment. Math. Helv. 51 (1976), no. 1, 43–55. MR 397805, DOI 10.1007/BF02568142
Joseph Hersch, Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1645–A1648 (French). MR 292357