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arXiv · 2610.20406

CMC foliations on Euclidean spaces are minimal foliations

José Edson Sampaio·Euripedes Carvalho da Silva
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Abstract

In this article, we provide a complete answer to one of the most classical conjectures in differential geometry (of foliations). More precisely, we present a complete positive answer to the classical conjecture, due to Meeks III, Pérez, and Ros (2008), that states that every foliation on $\mathbb{R}^{n+1}$ by (possibly varying) CMC hypersurfaces is a foliation by minimal hypersurfaces. Moreover, if $n\leq 6$, such a CMC foliation must consist of parallel hyperplanes.

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José Edson Sampaio, Euripedes Carvalho da Silva. 2026-10-14. CMC foliations on Euclidean spaces are minimal foliations. https://arxiv.org/abs/2610.20406

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