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Successive radii and ball operators in generalized Minkowski spaces

  • Thomas Jahn EMAIL logo
Published/Copyright: July 22, 2017
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Advances in Geometry
From the journal Advances in Geometry Volume 17 Issue 3

Abstract

We introduce successive radii in generalized Minkowski spaces (that is, with respect to gauges) and study some first properties. 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, we also look at ball intersections and ball hulls.

Keywords: Ball hull; ball intersection; containment problem; convex distance function; gauge; generalized Minkowski space; Minkowski functional; successive radii
MSC 2010: 52A21; 52A27; 52A40

Communicated by: M. Henk

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Received: 2015-4-13
Revised: 2015-7-27
Revised: 2015-9-25
Published Online: 2017-7-22
Published in Print: 2017-7-26

© 2017 by Walter de Gruyter Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  3. Classification of 3-dimensional left-invariant almost paracontact metric structures
  5. On the topology of the spaces of curvature constrained plane curves
  7. On deformations of parallel G2 structures and almost contact metric structures
  9. A flag representation of projection functions
  11. A fundamental theorem for submanifolds of multiproducts of real space forms
  13. Intriguing sets of quadrics in PG(5, q)
  15. Successive radii and ball operators in generalized Minkowski spaces
  17. Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
  19. The Archimedean projection property
  21. Kernels of numerical pushforwards
  23. Modified classical flat Minkowski planes
https://doi.org/10.1515/advgeom-2017-0012
Keywords for this article
Ball hull; ball intersection; containment problem; convex distance function; gauge; generalized Minkowski space; Minkowski functional; successive radii

Articles in the same Issue

  1. Frontmatter
  3. Classification of 3-dimensional left-invariant almost paracontact metric structures
  5. On the topology of the spaces of curvature constrained plane curves
  7. On deformations of parallel G2 structures and almost contact metric structures
  9. A flag representation of projection functions
  11. A fundamental theorem for submanifolds of multiproducts of real space forms
  13. Intriguing sets of quadrics in PG(5, q)
  15. Successive radii and ball operators in generalized Minkowski spaces
  17. Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms
  19. The Archimedean projection property
  21. Kernels of numerical pushforwards
  23. Modified classical flat Minkowski planes
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