An improved bound on the Minkowski dimension of Besicovitch sets in R3

A Besicovitch set is a set which contains a unit line segment in any direction. It is known that the Minkowski and Hausdorff dimensions of such a set must be greater than or equal to 5/2 in R-3. In this paper we show that the Minkowski dimension must in fact be greater than 5/2 + epsilon for some absolute constant epsilon > 0. One observation arising from the argument is that Besicovitch sets of near-minimal dimension have to satisfy certain strong properties, which we call "stickiness," "planiness," and "graininess."