Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-29T12:35:28.388Z Has data issue: false hasContentIssue false
  • English
  • Français

Isometries of the space of convex bodies of Ed

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Peter M. Gruber
Peter M. Gruber
Affiliation:
Institut für Analysis, Technische Universität Wien, A-1040 Wien, GuBhausstr. 27–29.
Get access

Abstract

The isometries of the space of convex bodies of Ed with respect to the symmetric-difference metric are precisely the mappings generated by measurepreserving affinities of Ed.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)

Information

Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 270 - 278
Copyright
Copyright © University College London 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Buchmann, E. and Valentine, F. A.. “A characterization of the parallelepiped in En”, Pacific J. Math., 35 (1970), 53–57.CrossRefGoogle Scholar
2.Dinghas, A.. “Über das Verhalten der Entfernung zweier Punktmengen bei gleichzeitiger Symmetrisierung derselben”, Arch. Math., 8 (1957), 46–57.CrossRefGoogle Scholar
3.Gruber, P. M.. “Isometrien des Konvexringes”, submitted.Google Scholar
4.Gruber, P. M.. “The space of compact subsets of Ed”, Geometriae DedicataGoogle Scholar
5.Rogers, C. A.. Hausdorff measures (Cambridge University Press, 1970).Google Scholar
6.Schneider, R.. “Isometrien des Raumes der konvexen Korper”, Colloquium Math., 33 (1975), 219–224.CrossRefGoogle Scholar
7.Shephard, G. C. and Webster, R. J.. “Metrics for sets of convex bodies”, Mathematika, 12 (1965), 73–88.CrossRefGoogle Scholar