Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 11 (2013), 1895-1922.
On the inverse Klain map
The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its Klain function is characterized. Among several applications, it is shown that McMullen’s decomposition is not possible in the class of translation-invariant, continuous, positive valuations. This implies that there exists no McMullen decomposition for translation-invariant, continuous Minkowski valuations, which solves a problem first posed by Schneider and Schuster.
Duke Math. J., Volume 162, Number 11 (2013), 1895-1922.
First available in Project Euclid: 8 August 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Secondary: 52B45: Dissections and valuations (Hilbert's third problem, etc.) 52A40: Inequalities and extremum problems
Parapatits, Lukas; Wannerer, Thomas. On the inverse Klain map. Duke Math. J. 162 (2013), no. 11, 1895--1922. doi:10.1215/00127094-2333971. https://projecteuclid.org/euclid.dmj/1375966905