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On some variants of the Kakeya problem

Kolasa, Lawrence and Wolff, Thomas (1999) On some variants of the Kakeya problem. Pacific Journal of Mathematics, 190 (1). pp. 111-154. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:KOLpjm99

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Abstract

We study the question of lower bounds for the Hausdorff dimension of a set in R-n containing spheres of every radius. If n greater than or equal to 3 then such a set must have dimension n. If n = 2 then it must have dimension at least 11/6. We also study the analogous maximal function problem and related problem of Besicovitch sets with an axis of symmetry.


Item Type:Article
Additional Information:© Copyright 1999 Pacific Journal of Mathematics. Received January 22, 1996 and revised May 20, 1997. The second author was supported by DMS 93-07872.
Record Number:CaltechAUTHORS:KOLpjm99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KOLpjm99
Alternative URL:http://pjm.math.berkeley.edu/1999/190-1/p06.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:710
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Sep 2005
Last Modified:26 Dec 2012 08:41

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