PreprintCC BY 4.0arXiv
Mean curvature bounds for CMC foliations of manifolds with sectional curvature bounded below
Abstract
Let Mn+1 be a complete Riemannian manifold with secM≥−K0, K0≥0, and let F be a codimension one foliation of M by hypersurfaces of constant mean curvature, the constant depending on the leaf. We prove that the mean curvature of every leaf satisfies |H|≤(n+1)√(K0). In particular, the mean curvature of the leaves of a CMC foliation of a complete manifold with |secM|≤1 is bounded by n+1, which answers positively a conjecture of Meeks III, Pérez, and Ros.
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BibTeX
@misc{sampaio2026mean,
title = {{Mean curvature bounds for CMC foliations of manifolds with sectional curvature bounded below}},
author = {José Edson Sampaio and Euripedes Carvalho da Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42093},
eprint = {2610.42093},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42093},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mean curvature bounds for CMC foliations of manifolds with sectional curvature bounded below
AU - José Edson Sampaio
AU - Euripedes Carvalho da Silva
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42093
UR - https://arxiv.org/abs/2610.42093
AB - Let M^n+1 be a complete Riemannian manifold with sec_M≥−K_0, K_0≥0, and let F be a codimension one foliation of M by hypersurfaces of constant mean curvature, the constant depending on the leaf. We prove that the mean curvature of every leaf satisfies |H|≤(n+1)√(K_0). In particular, the mean curvature of the leaves of a CMC foliation of a complete manifold with |sec_M|≤1 is bounded by n+1, which answers positively a conjecture of Meeks III, Pérez, and Ros.
ER -