The mixed affine quermassintegrals
Chang-Jian Zhao
TL;DR
This paper introduces mixed affine quermassintegrals, establishes their Aleksandrov-Fenchel inequality, and derives Minkowski and Brunn-Minkowski inequalities as applications, advancing the understanding of affine geometric measures.
Contribution
The paper presents the first definition of mixed affine quermassintegrals and proves fundamental inequalities for these measures, extending classical affine geometry results.
Findings
Established the Aleksandrov-Fenchel inequality for mixed affine quermassintegrals.
Derived Minkowski and Brunn-Minkowski inequalities for these measures.
Extended classical affine geometric inequalities to new mixed measures.
Abstract
In this paper, we introduce first the mixed affine quermassintegrals. The Aleksandrov-Fenchel inequality for the mixed affine quermassintegrals is established. As an application, the Minkowski, Brunn-Minkowski inequalities for the mixed affine quermassintegrals are also derived.
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Taxonomy
TopicsPoint processes and geometric inequalities · Computational Geometry and Mesh Generation · Advanced Combinatorial Mathematics