Minkowski valuations
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- by Monika Ludwig
- Trans. Amer. Math. Soc. 357 (2005), 4191-4213
- DOI: https://doi.org/10.1090/S0002-9947-04-03666-9
- Published electronically: October 28, 2004
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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.References
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Bibliographic Information
- Monika Ludwig
- Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria
- MR Author ID: 353373
- Email: monika.ludwig@tuwien.ac.at
- Received by editor(s): December 17, 2003
- Published electronically: October 28, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 4191-4213
- MSC (2000): Primary 52A20; Secondary 52B11, 52B45
- DOI: https://doi.org/10.1090/S0002-9947-04-03666-9
- MathSciNet review: 2159706