An improved bound on the Minkowski dimension of Besicovitch sets in R^3
| dc.creator | Katz, Nets Hawk | |
| dc.creator | Łaba, Izabella | |
| dc.creator | Tao, Terence | |
| dc.date | 1999-03-29 | |
| dc.date | 2000-09-01 | |
| dc.date.accessioned | 2026-07-07T05:28:31Z | |
| dc.date.available | 2026-07-07T05:28:31Z | |
| dc.description | 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 + εfor some absolute constant ε> 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.'' The purpose of this paper is to improve upon the known bounds for the Minkowski dimension of Besicovitch sets in three dimensions. As a by-product of the argument we obtain some strong conclusions on the structure of Besicovitch sets with almost-minimal Minkowski dimension. | |
| dc.description | 64 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/9903166 | |
| dc.identifier | http://arxiv.org/abs/math/9903166 | |
| dc.identifier | Ann. of Math. (2) 152 (2000), no. 2, 383-446 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78284 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B15 | |
| dc.title | An improved bound on the Minkowski dimension of Besicovitch sets in R^3 | |
| dc.type | text |