analysis / Spectral geometry

The Planar Steklov Analogue of Kac's Question

Strict convexity and real-analytic boundaries are what make this sharp: the classical Gordon-Webb-Wolpert drums are non-convex polygons, so the obvious escape routes are closed off.

25Significance / 100
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analysisAug 11, 2026Significance 25/100Registry: unreviewed

The Planar Steklov Analogue of Kac's Question

Prior state unknown→disproved

Strict convexity and real-analytic boundaries are what make this sharp: the classical Gordon-Webb-Wolpert drums are non-convex polygons, so the obvious escape routes are closed off.

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Strict convexity and real-analytic boundaries are what make this sharp: the classical Gordon-Webb-Wolpert drums are non-convex polygons, so the obvious escape routes are closed off.

Strict convexity and real-analytic boundaries are what make this sharp: the classical Gordon-Webb-Wolpert drums are non-convex polygons, so the obvious escape routes are closed off.

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The Planar Steklov Analogue of Kac's Question — Mathematical Frontier Network