Aleksandrov-Fenchel inequality for coconvex bodies
Askold Khovanskii, Vladlen Timorin
TL;DR
This paper extends the Aleksandrov-Fenchel inequality to coconvex bodies, linking convex geometry with algebraic concepts, and provides a new inequality inspired by commutative algebra.
Contribution
It introduces a novel version of the Aleksandrov-Fenchel inequality applicable to coconvex bodies, bridging convex geometry and algebraic intersection theory.
Findings
Established a new inequality for mixed volumes of coconvex bodies
Connected convex geometric inequalities with algebraic intersection multiplicities
Provided theoretical foundations for further research in convex and algebraic geometry
Abstract
We prove a version of the Aleksandrov-Fenchel inequality for mixed volumes of coconvex bodies. This version is motivated by an inequality from commutative algebra relating intersection multiplicities of ideals.
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Inequalities and Applications · Advanced Banach Space Theory