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



Anandateertha Mangasuli


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.


Laplace operator, eigenvalues, Legendre polynomials

2010 Mathematics Subject Classification

Primary 58J50. Secondary 34B30.

Published 1 January 2009