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arXiv · 2601.16966

Stability inequalities for one-phase cones

Benjy Firester·Raphael Tsiamis·Yipeng Wang
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Abstract

We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension $7$ and above, cohomogeneity one solutions with bi-orthogonal symmetry are strictly stable. As a consequence, we obtain a bound on the first eigenvalue and the decay rates of Jacobi fields, with applications to the generic regularity of the one-phase problem.

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Benjy Firester, Raphael Tsiamis, Yipeng Wang. 2026-01-23. Stability inequalities for one-phase cones. https://arxiv.org/abs/2601.16966

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