A characterization of constant width in Minkowski planes
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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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