{"id":"hexagon/2610.00629","pdf":"https://hexagonmath.org/pdf/2610.00629v1","url":"https://hexagonmath.org/abs/2610.00629v1","tags":["math.CA","msc:52A20","Ulam's floating body problem","bodies of revolution","central symmetry","convex geometry","floating bodies","small divisors"],"score":0,"title":"Analytic symmetric floating bodies","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["Liam Price","Tom de Groot"],"reviews":0,"subject":"math.MG","summary":"In every dimension $d\\ge3$, we construct nonspherical, origin-symmetric, strictly convex bodies of revolution with real-analytic boundary that float in equilibrium in every orientation. Their densities tend to the unit-ball cap fraction at height $(d+4)^{-1/2}$, where we prove that a degree-four spherical resonance is isolated. More generally, our construction applies at isolated even-degree resonances whose waterline angle is an irrational multiple of $\\pi$. Varying the density gives formal deformations. To obtain actual bodies, we use a finite-order diagonal reduction to establish inverse…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}