Proceedings of the American Mathematical Society

Author(s): Chung-Tsun Shieh
Journal: Proc. Amer. Math. Soc. 132 (2004), 157-164.
MSC (2000): Primary 35P15
Posted: 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

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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