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Quermassintegral inequalities for capillary hypersurfaces in a horoball
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≤ l<k≤ 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∈(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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BibTeX
@misc{guo2026quermassintegral,
title = {{Quermassintegral inequalities for capillary hypersurfaces in a horoball}},
author = {Jinyu Guo and Liangjun Weng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30771},
eprint = {2610.30771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30771},
}
RIS
TY - UNPB
TI - Quermassintegral inequalities for capillary hypersurfaces in a horoball
AU - Jinyu Guo
AU - Liangjun Weng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30771
UR - https://arxiv.org/abs/2610.30771
AB - 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≤ l<k≤ 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∈(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.
ER -