Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
arXiv:2408.13655 · doi:10.1007/s00209-025-03781-z
Abstract
In this paper, we provide an affirmative answer to [16, Conjecture 1.5] on the Alexandrov-Fenchel inequality for quermassintegrals for convex capillary hypersurfaces in the Euclidean half-space. More generally, we establish a theory for capillary convex bodies in the half-space and prove a general Alexandrov-Fenchel inequality for mixed volumes of capillary convex bodies. The conjecture [16, Conjecture 1.5] follows as its consequence.
Final version, to appear in Math. Z
References in corpus (6)
- Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
- Heintze-Karcher inequality and capillary hypersurfaces in a wedge
- A constrained mean curvature flow and Alexandrov-Fenchel inequalities
- A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
- A Minkowski-type inequality for capillary hypersurfaces in a half-space
- A fully nonlinear locally constrained curvature flow for capillary hypersurface