{"id":"palomar/PALOMAR-2026-10-27-000029","url":"https://github.com/QuanyuTang/steklov-isospectral-formalization/tree/54fddf140bb5fb86ce2eb8fceddb46f20bac1842","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000029-v1.json","repo":"https://github.com/QuanyuTang/steklov-isospectral-formalization","tags":["math.SP","math.DG","msc:58J53","msc:58J50","msc:30C35"],"score":0,"title":"Strictly Convex Steklov-Isospectral Plane Domains","trust":"high","domain":"math.SP","source":"palomar","authors":["taohu-hub","RGConj","QuanyuTang"],"reviews":0,"subject":"math.SP","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true,"formalizes":[{"title":"Strictly Convex Steklov-Isospectral Plane Domains","identifier":"https://arxiv.org/abs/2608.10557v2","relationship":"adapts"}]}