Year: 2026
Type: preprint
Abstract: We prove that a connected mean convex region in $\mathbb{R}^{n+1}$ with at least two boundary 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.
Source: arXiv (Cornell University)
Author: Xue, Haotian
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161771643