Skip to main content Accessibility help
×
Home

Covering convex bodies by translates of convex bodies

  • C. A. Rogers (a1) and C. Zong (a2)

Abstract

A number of known estimates of the number of translates, or lattice translates, of a convex body H required to cover a convex body K are obtained as consequences of two simple results.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Covering convex bodies by translates of convex bodies
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Covering convex bodies by translates of convex bodies
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Covering convex bodies by translates of convex bodies
      Available formats
      ×

Copyright

References

Hide All
1.Bezdek, K.. Hadwiger Levi's covering problem revisited. New Trends in Discrete and Computational Geometry (Pach, J., ed.) (Springer-Verlag, Berlin, 1994), pp. 199233.
2.Bezdek, K.. On affine subspaces that illuminate a convex set. Beitrdge Algebra Geom., 35 (1994), 131139.
3.Boltjanski, V. G. and Gohberg, I.. Results and Problems in Combinatorial Geometry (Cambridge University Press, 1985).
4.Chakerian, G. D. and Stein, S. K.. On the measures of symmetry of convex bodies. Canad. J. Math., 17 (1965), 497504.
5.Grünbaum, B.. Measures of symmetry for convex sets. Proc. Svmpos. Pure Math., 1 (1963), 233270.
6.Hadwiger, H.. Ungeloste Problems no. 20. Elem. Math., 12 (1957), 121.
7.Rogers, C. A.. A note on coverings. Mathematika, 4 (1957), 16.
8.Rogers, C. A.. Lattice coverings of space. Mathematika, 6 (1959), 3339.
9.Rogers, C. A.. Packing and Covering (Cambridge University Press, 1964).
10.Rogers, C. A. and Shephard, G. C.. The difference body of a convex body. Arch. Math., 8 (1958), 220233.
11.Zong, C.. Some remarks concerning kissing numbers, blocking numbers and covering numbers. Period. Math. Hungar., 30 (1995), 233–23
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Covering convex bodies by translates of convex bodies

  • C. A. Rogers (a1) and C. Zong (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed