Mathematics > Differential Geometry
arXiv:2605.19679 (math)
[Submitted on 19 May 2026 (v1), last revised 27 May 2026 (this version, v2)]
Abstract: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.
Submission history
From: Haotian Xue [view email]
[v1]
Tue, 19 May 2026 11:10:27 UTC (14 KB)
[v2]
Wed, 27 May 2026 11:41:34 UTC (13 KB)
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