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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minkowski valuations


Author: Monika Ludwig
Journal: Trans. Amer. Math. Soc. 357 (2005), 4191-4213
MSC (2000): Primary 52A20; Secondary 52B11, 52B45
Published electronically: October 28, 2004
MathSciNet review: 2159706
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Abstract | References | Similar Articles | Additional Information

Abstract: Centroid and difference bodies define $\operatorname{SL}(n)$ equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of $\operatorname{SL}(n)$equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of $\operatorname{SL}(n)$contravariant Minkowski valuations and of $L_p$-Minkowski valuations.


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Additional Information

Monika Ludwig
Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria
Email: monika.ludwig@tuwien.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03666-9
PII: S 0002-9947(04)03666-9
Received by editor(s): December 17, 2003
Published electronically: October 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society