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Journal of Geometry

, 110:3 | Cite as

Immobilization of convex bodies in \({\mathbb {R}}^n\)

  • Anthony David GilbertEmail author
  • Saul Hannington Nsubuga
Open Access
Article
  • 81 Downloads

Abstract

We extend to arbitrary finite n the notion of immobilization of a convex body O in \({\mathbb {R}}^n\) by a finite set of points \({\mathcal {P}}\) in the boundary of O. Because of its importance for this problem, necessary and sufficient conditions are found for the immobilization of an n-simplex. A fairly complete geometric description of these conditions is given: as n increases from \(n = 2\), some qualitative difference in the nature of the sets \({\mathcal {P}}\) emerges.

Keywords

Immobilization n-simplex contact points 

Mathematics Subject Classification

Primary 52A20 Secondary 52A15 

Notes

Acknowledgements

The authors wish to thank Elmer Rees for his generous advice towards this paper.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Anthony David Gilbert
    • 1
    Email author
  • Saul Hannington Nsubuga
    • 2
  1. 1.School of MathematicsThe University of EdinburghEdinburghUK
  2. 2.Department of MathematicsMakerere UniversityKampalaUganda

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