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$ \mathrm{GL}(n)$ contravariant Minkowski valuations


Authors: Franz E. Schuster and Thomas Wannerer
Journal: Trans. Amer. Math. Soc. 364 (2012), 815-826
MSC (2010): Primary 52A20; Secondary 52B45, 52A40
Published electronically: October 4, 2011
MathSciNet review: 2846354
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Abstract: A complete classification of all continuous $ \mathrm {GL}(n)$ contravariant Minkowski valuations is established. As an application we present a family of sharp isoperimetric inequalities for such valuations which generalize the classical Petty projection inequality.


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Additional Information

Franz E. Schuster
Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10/1046, A–1040 Vienna, Austria
Email: franz.schuster@tuwien.ac.at

Thomas Wannerer
Affiliation: Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10/1046, A–1040 Vienna, Austria
Email: thomas.wannerer@tuwien.ac.at

DOI: https://doi.org/10.1090/S0002-9947-2011-05364-X
Received by editor(s): February 16, 2010
Published electronically: October 4, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.