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Published September 1, 1999 | public
Journal Article Open

On some variants of the Kakeya problem

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.

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.

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August 22, 2023
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