Steklov rigidity of Euclidean balls

Romain Speciel

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arXiv · 2608.05577

Steklov rigidity of Euclidean balls

Romain Speciel

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Abstract

Let $\Omega\subset \mathbb{R}^n$, $n\geq 3$, be a bounded domain with smooth boundary. We show that if the Steklov spectrum of $\Omega$ tends to that of a ball at a sufficiently fast rate, then $\Omega$ must itself be a ball. In particular, in any dimension and among all bounded domains with smooth and possibly disconnected boundary, Euclidean balls are uniquely determined by their Steklov spectrum.

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Romain Speciel. 2026-08-06. Steklov rigidity of Euclidean balls. https://arxiv.org/abs/2608.05577

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