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2017 Extremal radii, diameter and minimum width in generalized Minkowski spaces
Thomas Jahn
Rocky Mountain J. Math. 47(3): 825-848 (2017). DOI: 10.1216/RMJ-2017-47-3-825

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.

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Thomas Jahn. "Extremal radii, diameter and minimum width in generalized Minkowski spaces." Rocky Mountain J. Math. 47 (3) 825 - 848, 2017. https://doi.org/10.1216/RMJ-2017-47-3-825

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 1369.52010
MathSciNet: MR3682151
Digital Object Identifier: 10.1216/RMJ-2017-47-3-825

Subjects:
Primary: 52A21, 52A27, 52A40

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 3 • 2017
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