A characterization of constant width in Minkowski planes

• Autores: Gennadiy Averkov , Horst Martini
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 68, Nº. 1-2, 2004, págs. 38-45
• Idioma: inglés
• DOI: 10.1007/s00010-003-2723-5
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• Resumen

  • 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.