Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-13T12:11:09.563Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Remarks on Translative Coverings of Convex Domains by Strips

Published online by Cambridge University Press:  20 November 2018

H. Groemer
H. Groemer*
Affiliation:
Department of Mathematics, The University of ArizonaTucson, AZ 85721, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the euclidean plane let K be a compact convex set and Sl, S2,… strips of respective widths wl, w2,… Some conditions on Σ wi are given that imply that K can be covered by translates of the strips Si. These conditions involve the perimeter, the diameter, or the minimal width of K and yield improvements of previously known results.

Keywords

52A45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 233 - 237
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Firey, W. J. and Groemer, H., Convex polyhedra which cover a convex set. J. London Math. Soc. 39 (1964), 261–266.Google Scholar
2. Groemer, H., On coverings of plane convex sets by translates of strips. Aequationes Math. 22 (1981), 215–222.Google Scholar
3. Groemer, H., On coverings of convex sets by translates of slabs. Proc. Amer. Math. Soc. 82 (1981), 261–266.Google Scholar
4. Groemer, H., Covering and packing properties of bounded sequences of convex sets. Mathematika 29 (1982), 18–31.Google Scholar
5. Makai, E. Jr, and Pach, J., Controlling function classes and covering of Euclidean space. To appear.Google Scholar