On the second eigenvalue of the Laplace operator on a spherical band
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 the second eigenvalue is maximized at the band which is symmetrical with respect to the equator.
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Affiliation: Department of Mathematics, Fu-Jen Catholic University, Taipei, Taiwan, Republic of China
Received by editor(s): April 27, 2001
Received by editor(s) in revised form: July 8, 2002, and August 21, 2002
Published electronically: May 8, 2003
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society