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arXiv · 2605.07913

Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric

Xavier Fernández-Real·Enric Florit-Simon·Joaquim Serra
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Abstract

We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4 \le n \le 6$ in which stable entire solutions are shown to be flat.

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Xavier Fernández-Real, Enric Florit-Simon, Joaquim Serra. 2026-05-08. Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric. https://arxiv.org/abs/2605.07913

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