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Bibliographic Details
Main Author: Xue, Haotian
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.19679
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author Xue, Haotian
author_facet Xue, Haotian
contents We prove that a connected mean convex region in $\mathbb{R}^{n+1}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_19679
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Frankel type theorem in Euclidean and hyperbolic spaces
Xue, Haotian
Differential Geometry
We prove that a connected mean convex region in $\mathbb{R}^{n+1}$ 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.
title A Frankel type theorem in Euclidean and hyperbolic spaces
topic Differential Geometry
url https://arxiv.org/abs/2605.19679