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$ \mathrm{SL}(n)$-contravariant $ L_p$-Minkowski valuations


Author: Lukas Parapatits
Journal: Trans. Amer. Math. Soc. 366 (2014), 1195-1211
MSC (2010): Primary 52A20, 52B45
DOI: https://doi.org/10.1090/S0002-9947-2013-05750-9
Published electronically: August 19, 2013
MathSciNet review: 3145728
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Abstract: All $ \operatorname {SL}(n)$-contravariant $ L_p$-Minkowski valuations on polytopes are completely classified. The prototypes of such valuations turn out to be the asymmetric $ L_p$-projection body operators.


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Additional Information

Lukas Parapatits
Affiliation: Fachbereich Mathematik, Universität Salzburg, Hellbrunner Str. 34, 5020 Salzburg, Austria
Address at time of publication: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-70/704, 7040 Wien, Austria
Email: lukas.parapatits@sbg.ac.at, lukas.parapatits@tuwien.ac.at

DOI: https://doi.org/10.1090/S0002-9947-2013-05750-9
Received by editor(s): August 29, 2011
Received by editor(s) in revised form: November 7, 2011
Published electronically: August 19, 2013
Additional Notes: The author was supported by Austrian Science Fund (FWF): P22388 and Austrian Science Fund (FWF): P23639
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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