On the best constant for the besicovitch covering theorem

Z. Füredi, Peter A. Loeb

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.

Original languageEnglish
Pages (from-to)1063-1073
Number of pages11
JournalProceedings of the American Mathematical Society
Volume121
Issue number4
DOIs
Publication statusPublished - 1994

Fingerprint

Best Constants
Covering
Ball
Theorem
Upper and Lower Bounds
Radius
Closed

Keywords

  • Besicovitch Covering Theorem
  • Proximity graphs
  • Sphere packings

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the best constant for the besicovitch covering theorem. / Füredi, Z.; Loeb, Peter A.

In: Proceedings of the American Mathematical Society, Vol. 121, No. 4, 1994, p. 1063-1073.

Research output: Contribution to journalArticle

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