  We study the eigenvalues of the Laplacian on ellipsoids that are obtained as
perturbations of the standard Euclidean unit sphere in dimension two. A
comparison of these eigenvalues with those of the standard Euclidean unit
sphere is obtained under a Gaussian curvature condition, in line with the
Lichnerowicz theorem on the first positive eigenvalue on a compact Riemannian
manifold.
