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<p>In this paper, we provide an affirmative answer to [<CitationRef CitationID="CR16">16</CitationRef>, 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 [<CitationRef CitationID="CR16">16</CitationRef>, Conjecture 1.5] follows as its consequence.</p>

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Alexandrov–Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月26日

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  • Xinqun Mei,
  • Guofang Wang,
  • Liangjun Weng,
  • Chao Xia

摘要

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.