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

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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Published 1 January 2009