A product integral representation of mixed volumes of two convex bodies

Details A product integral representation of mixed volumes of two convex bodies A product integral representation of mixed volumes of two convex bodies

2011-11-30

arxiv.org/abs/1112.0955v1

Mathematics

Metric Geometry

Scientific paper

The Brunn-Minkowski theory relies heavily on the notion of a mixed volume. 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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