On the best constant for the Besicovitch covering theorem
Authors:
- Zoltán FürediZFZoltán Füredi
- Peter A. LoebPLPeter A. Loeb
- 1 January 1994
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 121 (4) , 1063-1073
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.Keywords
This publication has 24 references indexed in Scilit:
- An Optimization of the Besicovitch CoveringProceedings of the American Mathematical Society, 1993
- Antisocial Subcovers of Self-Centered CoveringsThe American Mathematical Monthly, 1986
- Relative neighborhood graphs in the Li-metricPattern Recognition, 1985
- Almost Euclidean Quotient Spaces of Subspaces of a Finite-Dimensional Normed SpaceProceedings of the American Mathematical Society, 1985
- REMARKS ON THE SPHERE OF INFLUENCE GRAPHAnnals of the New York Academy of Sciences, 1985
- A Variant of the Problem of the Thirteen SpheresCanadian Journal of Mathematics, 1967
- Extremal lattices of convex bodiesMathematical Proceedings of the Cambridge Philosophical Society, 1953
- Geometrical Extrema Suggested by a Lemma of BesicovitchThe American Mathematical Monthly, 1951
- A Problem on CirclesThe Mathematical Gazette, 1948
- Perfect BlanketsTransactions of the American Mathematical Society, 1947