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Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
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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.
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Cited by 3 Pith papers
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Capillary curvature images
The authors solve the even capillary L_p-Minkowski problem for -n < p < 1, proving existence of smooth even capillary hypersurfaces with prescribed curvature in the half-space.
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The capillary $L_p$-Minkowski problem
Existence of smooth convex capillary bodies with prescribed capillary L_p-surface area measure is proved for all p>1, with a symmetry condition needed when 1<p<n+1.
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Convex capillary hypersurfaces of prescribed curvature problem
A strictly convex capillary hypersurface with prescribed k-th Weingarten curvature exists whenever the prescribed data is symmetric under horizontal reflection.
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