Abstract

We study the question of lower bounds for the Hausdorff dimension of a set in Rⁿ containing spheres of every radius. If n ≥ 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.

Authors