Strictly Convex Steklov-Isospectral Plane Domains

Tao Hu; Jiachen Shi; Quanyu Tang

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arXiv · 2608.10557

Strictly Convex Steklov-Isospectral Plane Domains

Tao Hu·Jiachen Shi·Quanyu Tang

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Abstract

We construct pairs of noncongruent bounded Euclidean plane domains with identical Steklov spectra, including multiplicities. This gives a negative answer to the planar Steklov analogue of Kac's question ``Can one hear the shape of a drum?'' The domains are simply connected and strictly convex, have real-analytic boundaries, and may be chosen arbitrarily close to a disk in the $C^\infty$ topology.

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BibTeX RIS

Tao Hu, Jiachen Shi, Quanyu Tang. 2026-08-11. Strictly Convex Steklov-Isospectral Plane Domains. https://arxiv.org/abs/2608.10557

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