English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study the spectrum of the Laplace-Beltrami operator on ellipsoids. Forellipsoids that are close to the sphere, we use analytic perturbation theory toestimate the eigenvalues up to two orders. We show that for biaxial ellipsoidssufficiently close to the sphere, the first $N$ eigenvalues have multiplicityat most two, and characterize those that are simple. For the triaxialellipsoids sufficiently close to the sphere that are not biaxial, we show thatat least the first sixteen eigenvalues are all simple.  We also give the results of various numerical experiments, includingcomparisons to our results from the analytic perturbation theory, andapproximations for the eigenvalues of ellipsoids that degenerate into infinitecylinders or two-dimensional disks. We propose a conjecture on the exact numberof nodal domains of near-sphere ellipsoids.

Laplace-Beltrami spectrum of ellipsoids that are close to spheres and analytic perturbation theory