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aequationes mathematicae

, Volume 68, Issue 1–2, pp 38–45 | Cite as

A characterization of constant width in Minkowski planes

  • Gennadiy Averkov
  • Horst Martini
Research paper
  • 38 Downloads

Summary.

Generalizing a result of A. Heppes [Hep59] we obtain the following characterization theorem: a convex body K in a Minkowski plane (i.e., in a real, two-dimensional Banach space) is of constant Minkowskian width if and only if every chord of it splits K into two compact sets such that one of them has diameter equal to the length of this chord.

Mathematics Subject Classification (2000).

52A10 52A21. 

Keywords.

Body of constant width Minkowski space Banach space Monotonicity lemma. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  • Gennadiy Averkov
    • 1
  • Horst Martini
    • 1
  1. 1.Faculty of MathematicsUniversity of TechnologyChemnitzGermany

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