An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension
| dc.creator | Laba, Izabella | |
| dc.creator | Tao, Terence | |
| dc.date | 2000-04-04 | |
| dc.date.accessioned | 2026-07-07T04:34:37Z | |
| dc.date.available | 2026-07-07T04:34:37Z | |
| dc.description | We use geometrical combinatorics arguments, including the ``hairbrush'' and x-ray arguments of Wolff and the sticky/plany/grainy analysis of Katz, Laba, and Tao, to show that Besicovitch sets in R^n have Minkowski dimension at least (n+2)/2 + \eps_n for all n > 3, where \eps_n > 0 is an absolute constant depending only on n. This complements the results of Katz, Laba, and Tao, which established the same result for n=3, and of Bourgain and Katz-Tao, arithmetic combinatorics techniques to establish the result for n > 8. In contrast to previous work, our arguments will be purely geometric and do not require arithmetic combinatorics. | |
| dc.description | 31 pages, 3 figures, submitted GAFA | |
| dc.identifier | https://arxiv.org/abs/math/0004015 | |
| dc.identifier | http://arxiv.org/abs/math/0004015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58969 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B25 | |
| dc.title | An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension | |
| dc.type | text |