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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Chung-Tsun Shieh
Journal: Proc. Amer. Math. Soc. 132 (2004), 157-164
MSC (2000): Primary 35P15
Published electronically: May 8, 2003
MathSciNet review: 2021258
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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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Additional Information

Chung-Tsun Shieh
Affiliation: Department of Mathematics, Fu-Jen Catholic University, Taipei, Taiwan, Republic of China
Email: ctshieh@math.fju.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07039-4
PII: S 0002-9939(03)07039-4
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