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A new construction of Radon curves and related topics

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Abstract

We present a new construction of Radon curves which only uses convexity methods. In other words, it does not rely on an auxiliary Euclidean background metric (as in the classical works of J. Radon, W. Blaschke, G. Birkhoff, and M. M. Day), and also it does not use typical methods from plane Minkowski Geometry (as proposed by H. Martini and K. J. Swanepoel). We also discuss some properties of normed planes whose unit circle is a Radon curve and give characterizations of Radon curves only in terms of Convex Geometry.

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Authors and Affiliations

  1. CEFET/RJ Campus Nova Friburgo, 28635-000, Nova Friburgo, Brazil

    Vitor Balestro

  2. Instituto de Matemática e Estatística, Universidade Federal Fluminense, 24020-140, Niterói, Brazil

    Vitor Balestro & Ralph Teixeira

  3. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Horst Martini

  4. Department of Applied Mathematics, Harbin University of Science and Technology, 150080, Harbin, China

    Horst Martini

Authors
  1. Vitor Balestro
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  2. Horst Martini
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  3. Ralph Teixeira
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Corresponding author

Correspondence to Vitor Balestro.

Additional information

V. Balestro thanks to CAPES for partial financial support during the preparation of this manuscript.

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Balestro, V., Martini, H. & Teixeira, R. A new construction of Radon curves and related topics. Aequat. Math. 90, 1013–1024 (2016). https://doi.org/10.1007/s00010-016-0423-1

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  • DOI: https://doi.org/10.1007/s00010-016-0423-1

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