Averkov, Gennadiy ; Martini, Horst : A characterization of constant width in Minkowski planes

Author(s):

Averkov, Gennadiy
Martini, Horst

Title:

A characterization of constant width in Minkowski planes

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 17, 2002

Mathematics Subject Classification:

52A21			[ Finite-dimensional Banach spaces ]
52A38			[ Length, area, volume ]
52A10			[ Convex sets in $2$ dimensions ]
52A20			[ Convex sets in $n$ dimensions ]

Abstract:

Generalizing a result of A.~Heppes we obtain the following characterization theorem: a convex body 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 the body into two compact sets so that one of them has diameter equal to the length of this chord. In addition, we give a suitable extension of the ``only if'' part of this theorem to higher dimensional Minkowski spaces.

Keywords:

body of constant (Minkowskian) width, diameter, section, hyperplane, Minkowski space

Language:

English

Publication time:

12 / 2002