A product integral representation of mixed volumes of two convex bodies
Daniel Hug, Jan Rataj, Wolfgang Weil
TL;DR
This paper introduces a new integral representation for mixed volumes of convex bodies using flag measures, enhancing the theoretical framework of the Brunn-Minkowski theory.
Contribution
It provides a novel product integral representation of mixed volumes in terms of flag measures, expanding explicit formulas beyond special cases.
Findings
New integral representation for mixed volumes
Connection between mixed volumes and flag measures
Enhanced understanding of convex geometry
Abstract
The Brunn-Minkowski theory relies heavily on the notion of mixed volumes. Despite its particular importance, even explicit representations for the mixed volumes of two convex bodies in Euclidean space are available only in special cases. Here we investigate a new integral representation of such mixed volumes, in terms of flag measures of the involved convex sets. A brief introduction to (extended) flag measures of convex bodies is also provided.
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