A Frankel type theorem in Euclidean and hyperbolic spaces
Differential Geometry
2026-05-28 v2
Abstract
We prove that a connected mean convex region in with at least two components cannot have strictly positive mean curvature. This answers a question of Gromov. We also obtain estimates for how quickly the mean curvature must decay at infinity, and generalize this result to hyperbolic space.
Cite
@article{arxiv.2605.19679,
title = {A Frankel type theorem in Euclidean and hyperbolic spaces},
author = {Haotian Xue},
journal= {arXiv preprint arXiv:2605.19679},
year = {2026}
}