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Ellipsoids

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Convexity and Its Applications

Abstract

Ellipsoids, which are the affine transforms of Euclidean balls, have many captivating properties and have been studied for their own intrinsic interest. Many extremal problems of an affine nature have ellipsoids as extremal bodies and this has motivated additional investigations. In studies of Minkowski geometries, Hilbert geometries, and affine differential geometry, ellipsoids play an important role. Known results on ellipsoids have been interpreted in the context of these geometries. On the other hand, problems formulated in these geometries have led to new results on ellipsoids.

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Authors
  1. Clinton M. Petty
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Editors and Affiliations

  1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Gusshausstrasse 25-27, A-1040, Wien, Austria

    Peter M. Gruber

  2. Lehrstuhl für Mathematik II, Universität Siegen, Hölderlinstrasse 3, D-5900, Siegen 21, Germany

    Jörg M. Wills

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© 1983 Springer Basel AG

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Petty, C.M. (1983). Ellipsoids. In: Gruber, P.M., Wills, J.M. (eds) Convexity and Its Applications. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5858-8_11

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  • DOI: https://doi.org/10.1007/978-3-0348-5858-8_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5860-1

  • Online ISBN: 978-3-0348-5858-8

  • eBook Packages: Springer Book Archive

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