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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The Centro-Affine Hadwiger Theorem
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by Christoph Haberl and Lukas Parapatits PDF
J. Amer. Math. Soc. 27 (2014), 685-705 Request permission

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
  • MR Author ID: 979076
  • Email: lukas.parapatits@tuwien.ac.at
  • Received by editor(s): February 23, 2012
  • Received by editor(s) in revised form: May 21, 2013
  • Published electronically: January 16, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 27 (2014), 685-705
  • MSC (2010): Primary 52A20, 52B45
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00781-5
  • MathSciNet review: 3194492