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Successive Radii and Ball Operators in Generalized Minkowski Spaces

2014/11/06 by Thomas Jahn, Jahn, Thomas
Mathematics · #52A21 #52A27 #52A40 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52A21 #msc:52A27 #msc:52A40

paper · pdf · doi:10.48550/arxiv.1411.1628

submitted to "Advances of Geometry"

arxiv created 2015/04/13 · arxiv updated 2015/04/14

Abstract

We investigate elementary properties of successive radii 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 minimal containment problems, where intersections or Minkowski sums of the latter set and affine flats of a certain dimension are incorporated. Since this is strongly related to minimax location problems and to the notions of diametrical completeness and constant width, we also have a look at ball intersections and ball hulls.

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