An improved bound on the Minkowski dimension of Besicovitch sets in R-3

A Besicovitch set is a set which contains a unit line segment in any direct ion. 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 ab solute constant epsilon > 0. One observation arising from the argument is t hat Besicovitch sets of near-minimal dimension have to satisfy certain stro ng properties, which we call "stickiness," "planiness," and "graininess."