Paper · Oct 22, 2026
Quermassintegral inequalities for capillary hypersurfaces in a horoball
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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 -th quermassintegral while monotonically increasing the -th quermassintegral for any . Using this flow, we establish a full family of the quermassintegral inequalities for horo-convex capillary hypersurfaces in a horoball with contact angle . Moreover, we weaken the horo-convexity to convexity and obtain the quermassintegral inequalities for convex capillary hypersurfaces between the -th and -th quermassintegrals.
Comments: 36 pages,1 figure
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