Quermassintegral inequalities for capillary hypersurfaces in a horoball

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 $(1\le l<k\le n)$. Using this flow, we establish a full family of the quermassintegral inequalities for horo-convex capillary hypersurfaces in a horoball with contact angle $\theta \in (0,\pi \mathrm{/}2]$. 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.