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Transactions of the American Mathematical Society

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Weighted floating bodies and polytopal approximation


Authors: Florian Besau, Monika Ludwig and Elisabeth M. Werner
Journal: Trans. Amer. Math. Soc. 370 (2018), 7129-7148
MSC (2010): Primary 52A38; Secondary 52A27, 52A55, 53C60, 60D05
DOI: https://doi.org/10.1090/tran/7233
Published electronically: April 4, 2018
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Abstract: 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
Email: besau@math.uni-frankfurt.de

Monika Ludwig
Affiliation: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria
Email: monika.ludwig@tuwien.ac.at

Elisabeth M. Werner
Affiliation: Department of Mathematics, Applied Mathematics and Statistics Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106
Email: elisabeth.werner@case.edu

DOI: https://doi.org/10.1090/tran/7233
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.
Article copyright: © Copyright 2018 American Mathematical Society

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