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arXiv · 2610.30771

Quermassintegral inequalities for capillary hypersurfaces in a horoball

Jinyu Guo·Liangjun Weng
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Abstract

In this paper, we study the quermassintegral inequalities for capillary hypersurfaces in a horoball in hyperbolic space. We construct a locally constrained nonlinear curvature flow that preserves the $k$-th quermassintegral while monotonically increasing the $l$-th quermassintegral for any $(1\leq l<k\leq n)$. Using this flow, we establish a full family of the quermassintegral inequalities for horo-convex capillary hypersurfaces in a horoball with contact angle $θ\in(0,π/2]$. Moreover, we weaken the horo-convexity to convexity and obtain the quermassintegral inequalities for convex capillary hypersurfaces between the $n$-th and $l$-th quermassintegrals.

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Jinyu Guo, Liangjun Weng. 2026-10-22. Quermassintegral inequalities for capillary hypersurfaces in a horoball. https://arxiv.org/abs/2610.30771

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