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arXiv · 2401.10743

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

Antoine Métras·Léonard Tschanz
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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 $n = 4$.

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Antoine Métras, Léonard Tschanz. 2024-01-19. Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space. https://doi.org/10.1080/10586458.2024.2410967

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