A Frankel type theorem in Euclidean and hyperbolic spaces

Haotian Xue

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arXiv · 2605.19679

A Frankel type theorem in Euclidean and hyperbolic spaces

Haotian Xue

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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.

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Haotian Xue. 2026-05-19. A Frankel type theorem in Euclidean and hyperbolic spaces. https://arxiv.org/abs/2605.19679

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