PreprintCC BY 4.0arXiv
CMC foliations on Euclidean spaces are minimal foliations
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 ℝn+1 by (possibly varying) CMC hypersurfaces is a foliation by minimal hypersurfaces. Moreover, if n≤ 6, such a CMC foliation must consist of parallel hyperplanes.
Related
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BibTeX
@misc{sampaio2026foliations,
title = {{CMC foliations on Euclidean spaces are minimal foliations}},
author = {José Edson Sampaio and Euripedes Carvalho da Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20406},
eprint = {2610.20406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20406},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CMC foliations on Euclidean spaces are minimal foliations
AU - José Edson Sampaio
AU - Euripedes Carvalho da Silva
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.20406
UR - https://arxiv.org/abs/2610.20406
AB - 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 ℝ^n+1 by (possibly varying) CMC hypersurfaces is a foliation by minimal hypersurfaces. Moreover, if n≤ 6, such a CMC foliation must consist of parallel hyperplanes.
ER -