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. https://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 | ||||||
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| 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. | ||||||
| Issue or Number: | 1 | ||||||
| Record Number: | CaltechAUTHORS:KOLpjm99 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:KOLpjm99 | ||||||
| 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: | 02 Oct 2019 22:36 |
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