Extremal radii, diameter and minimum width in generalized Minkowski spaces

Abstract

We discuss the notions of circumradius, inradius, diameter and minimum width in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the ``size'' of a given convex set in a finite-dimensional real vector space with respect to another convex set. This is done via formulating some kind of containment problem incorporating homothetic bodies of the latter set or strips bounded by parallel supporting hyperplanes thereof. This paper can be seen as a theoretical starting point for studying metric problems of convex sets in generalized Minkowski spaces.