The Planar Steklov Analogue of Kac's Question
Statement
Can one hear the shape of a drum, in the Steklov setting and in the plane? No: there exist pairs of noncongruent bounded plane domains with identical Steklov spectra including multiplicities, simply connected, strictly convex, with real-analytic boundaries, and arbitrarily close to a disk in the C-infinity topology.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Tao Hu, Jiachen Shi and Quanyu Tang, using ChatGPTThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The division of labour is set out in the AI statement: the idea of adapting the Sunada construction of Gordon, Webb and Wolpert to the planar Steklov problem "was proposed by the authors". From there, "ChatGPT provided substantial assistance in developing the concrete counterexample construction, including the passage from the orbifold construction to weighted Steklov problems on the disk and their subsequent realization by Euclidean plane domains. It also assisted with several technical arguments." The authors checked, revised and rewrote the arguments.
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