Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space

Abstract

We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Steklov eigenvalue is maximized, was exhibited and multiple questions were raised. In this article, we conjecture that, in any dimension, there is a finite number of infinite critical length. To investigate this, we develop an algorithm to efficiently perform numerical experiments, providing support to our conjecture. Furthermore, we prove the conjecture in dimension $n=3$ and $n=4$.

21 pages, including 6 pages of appendices

References in corpus (1)

• Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space