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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The Centro-Affine Hadwiger Theorem


Authors: Christoph Haberl and Lukas Parapatits
Journal: J. Amer. Math. Soc. 27 (2014), 685-705
MSC (2010): Primary 52A20, 52B45
Published electronically: January 16, 2014
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Abstract: All upper semicontinuous and $ \mathrm {SL}(n)$ invariant valuations on convex bodies containing the origin in their interiors are completely classified. Each such valuation is shown to be a linear combination of the Euler characteristic, the volume, the volume of the polar body, and the recently discovered Orlicz surface areas.


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Additional Information

Christoph Haberl
Affiliation: Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria
Email: christoph.haberl@gmail.com

Lukas Parapatits
Affiliation: Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstraße 8–10/104, 1040 Wien, Austria
Email: lukas.parapatits@tuwien.ac.at

DOI: http://dx.doi.org/10.1090/S0894-0347-2014-00781-5
PII: S 0894-0347(2014)00781-5
Received by editor(s): February 23, 2012
Received by editor(s) in revised form: May 21, 2013
Published electronically: January 16, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.