Asian Journal of Mathematics

On the Eigenvalues of the Laplacian for Certain Perturbations of the Standard Euclidean Metric on $S^2$

Anandateertha Mangasuli

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Abstract

We introduce certain conformal, rotationally symmetric, real analytic perturbations of the standard Euclidean metric on $S^2$ and study the perturbed eigenvalues of the Laplace operators for the metrics sufficiently close to the Euclidean metric.

Article information

Source
Asian J. Math., Volume 13, Number 2 (2009), 282-271.

Dates
First available in Project Euclid: 27 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1256650872

Mathematical Reviews number (MathSciNet)
MR2559111

Zentralblatt MATH identifier
1185.58014

Subjects
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 34B30: Special equations (Mathieu, Hill, Bessel, etc.)

Keywords
Laplace operator eigenvalues Legendre polynomials

Citation

Mangasuli, Anandateertha. On the Eigenvalues of the Laplacian for Certain Perturbations of the Standard Euclidean Metric on $S^2$. Asian J. Math. 13 (2009), no. 2, 282--271. https://projecteuclid.org/euclid.ajm/1256650872


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