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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Weighted floating bodies and polytopal approximation
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by Florian Besau, Monika Ludwig and Elisabeth M. Werner PDF
Trans. Amer. Math. Soc. 370 (2018), 7129-7148 Request permission


Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floating areas are combined to derive new asymptotic approximation results on the sphere, in hyperbolic space, and in Hilbert geometries.
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Additional Information
  • Florian Besau
  • Affiliation: Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Strasse 10, 60054 Frankfurt, Germany
  • MR Author ID: 1174501
  • ORCID: 0000-0002-6596-6127
  • Email:
  • Monika Ludwig
  • Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria
  • MR Author ID: 353373
  • Email:
  • Elisabeth M. Werner
  • Affiliation: Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106
  • MR Author ID: 252029
  • ORCID: 0000-0001-9602-2172
  • Email:
  • Received by editor(s): November 13, 2016
  • Received by editor(s) in revised form: March 1, 2017
  • Published electronically: April 4, 2018
  • Additional Notes: The authors thank Juan Carlos Alvarez Paiva and Matthias Reitzner for helpful discussions.
    The work of the second author was supported, in part, by Austrian Science Fund (FWF) Project P25515-N25.
    The third author was partially supported by NSF grant 1504701.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 7129-7148
  • MSC (2010): Primary 52A38; Secondary 52A27, 52A55, 53C60, 60D05
  • DOI:
  • MathSciNet review: 3841844