Asian Journal of Mathematics

Volume 13 (2009)

Number 2

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

Pages: 271 – 282

DOI: http://dx.doi.org/10.4310/AJM.2009.v13.n2.a6

Author

Anandateertha Mangasuli

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.

Keywords

Laplace operator; eigenvalues; Legendre polynomials

2010 Mathematics Subject Classification

Primary 58J50. Secondary 34B30.

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