Open Research Index

Strictly Convex Steklov-Isospectral Plane Domains

taohu-hub, RGConj, QuanyuTang

Palomar Registrypalomar/PALOMAR-2026-10-27-000029Oct 27, 2026math.SPscore 0

Formalization of a family of pairs of bounded, simply connected, strictly convex planar domains with real-analytic boundaries. At each parameter, the two domains have identical Steklov spectra, including multiplicities. Distinct labels or parameters give noncongruent domains. Each domain has perimeter 2π and no orientation-reversing Euclidean symmetry, and normalized conformal maps converge in C∞ to the identity. The proof uses an explicit degree-seven construction.

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