Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
A product integral representation of mixed volumes of two convex bodies
-
Daniel Hug
,
Jan Rataj
und
Wolfgang Weil
Veröffentlicht/Copyright:
1. Oktober 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.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- 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
Schlagwörter für diesen Artikel
Mixed volumes;
flag measures;
Grassmannian;
integral geometry;
generalized curvatures
Artikel in diesem Heft
- 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
