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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$\mathrm {GL}(n)$ contravariant Minkowski valuations
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by Franz E. Schuster and Thomas Wannerer PDF
Trans. Amer. Math. Soc. 364 (2012), 815-826 Request permission

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
  • MR Author ID: 764916
  • 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
  • Received by editor(s): February 16, 2010
  • Published electronically: October 4, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 815-826
  • MSC (2010): Primary 52A20; Secondary 52B45, 52A40
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05364-X
  • MathSciNet review: 2846354