Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric
Analysis of PDEs
2026-05-11 v1 Differential Geometry
Abstract
We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension in which stable entire solutions are shown to be flat.
Cite
@article{arxiv.2605.07913,
title = {Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric},
author = {Xavier Fernández-Real and Enric Florit-Simon and Joaquim Serra},
journal= {arXiv preprint arXiv:2605.07913},
year = {2026}
}