A characterization of constant width in Minkowski planes

Authors: Averkov, Gennadiy; Martini, Horst

Source: aequationes mathematicae, Volume 68, Numbers 1-2, August 2004 , pp. 38-45(8)

Publisher: Springer

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Abstract:

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.

Keywords: 52A10; 52A21; Body of constant width; Minkowski space; Banach space; Monotonicity lemma

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s00010-003-2723-5

Affiliations: 1: Faculty of Mathematics, University of Technology, D-09107, Chemnitz, Germany,

Publication date: 2004-08-01