On the second eigenvalue of the Laplace operator on a spherical band

Shieh, Chung-Tsun

doi:10.1090/S0002-9939-03-07039-4

On the second eigenvalue of the Laplace operator on a spherical band
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by Chung-Tsun Shieh

Proc. Amer. Math. Soc. 132 (2004), 157-164

DOI: https://doi.org/10.1090/S0002-9939-03-07039-4

Published electronically: May 8, 2003

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Abstract:

In this paper we prove that the second eigenvalue of the Laplacian for a spherical band on the unit sphere $S^2$ has multiplicity 2. We also show that among all spherical bands of given fixed area less than $2\pi$ the second eigenvalue is maximized at the band which is symmetrical with respect to the equator.

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