An improved bound on the Minkowsik dimension of Besicovitch sets in R^3

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 R3. In this paper we show that the Minkowski dimension must in fact be greater than 5/2 + " for some absolute constant " > 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.