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

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- 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.## References

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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