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On the minimal convex annulus of a planar convex body

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Abstract

In this paper we introduce the notion of a minimal convex annulusK (C) of a convex bodyC, generalizing the concept of a minimal circular annulus. Then we prove the existence — as for the minimal circular annulus — of a Radon partition of the set of contact points of the boundaries ofK (C) andC. Subsequently, the uniqueness ofK (C) is shown. Finally, it is proven that, for typicalC, the boundary ofC has precisely two points in common with each component of the boundary ofK (C).

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Authors and Affiliations

  1. Istituto di Matematica, Università Cattolica S. Cuore, Largo A Gemelli 1, 20123, Milano, Italy

    Carla Peri

  2. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Andreana Zucco

Authors
  1. Carla Peri
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  2. Andreana Zucco
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Peri, C., Zucco, A. On the minimal convex annulus of a planar convex body. Monatshefte für Mathematik 114, 125–133 (1992). https://doi.org/10.1007/BF01535579

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  • DOI: https://doi.org/10.1007/BF01535579

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