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Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space (2406.07304v2)
Published 11 Jun 2024 in math.DG and math.AP
Abstract: In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By constructing a new locally constrained inverse curvature flow, we obtain the Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in hyperbolic space. This generalizes a theorem of Brendle-Guan-Li \cite{BGL} for convex closed hypersurfaces in hyperbolic space.