Rocky Mountain Journal of Mathematics

Extremal radii, diameter and minimum width in generalized Minkowski spaces

Thomas Jahn

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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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 3 (2017), 825-848.

Dates
First available in Project Euclid: 24 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1498269813

Digital Object Identifier
doi:10.1216/RMJ-2017-47-3-825

Mathematical Reviews number (MathSciNet)
MR3682151

Zentralblatt MATH identifier
1369.52010

Subjects
Primary: 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx] 52A27: Approximation by convex sets 52A40: Inequalities and extremum problems

Keywords
Circumradius containment problem diameter gauge generalized Minkowski space inradius minimum width

Citation

Jahn, Thomas. Extremal radii, diameter and minimum width in generalized Minkowski spaces. Rocky Mountain J. Math. 47 (2017), no. 3, 825--848. doi:10.1216/RMJ-2017-47-3-825. https://projecteuclid.org/euclid.rmjm/1498269813


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