On the eigenvalues of the Laplacian on ellipsoids obtained as perturbation of unit sphere
arXiv:2201.07015 · doi:10.1007/s10455-023-09901-4
Abstract
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.
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