Analytic symmetric floating bodies
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…
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