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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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On the second eigenvalue of the Laplace operator on a spherical band
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by Chung-Tsun Shieh PDF
Proc. Amer. Math. Soc. 132 (2004), 157-164 Request permission

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
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 157-164
  • MSC (2000): Primary 35P15
  • DOI: https://doi.org/10.1090/S0002-9939-03-07039-4
  • MathSciNet review: 2021258