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A product integral representation of mixed volumes of two convex bodies
-
Daniel Hug
,
Jan Rataj
and
Wolfgang Weil
Published/Copyright:
October 1, 2013
Abstract
The Brunn-Minkowski theory in convex geometry 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 ℝd 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.
Published Online: 2013-10-01
Published in Print: 2013-10
© 2013 by Walter de Gruyter GmbH & Co.
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Keywords for this article
Mixed volumes;
flag measures;
Grassmannian;
integral geometry;
generalized curvatures
Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
