Some connections between Falconer's distance set conjecture, and sets of Furstenburg type
| dc.creator | Katz, Nets Hawk | |
| dc.creator | Tao, Terence | |
| dc.date | 2001-01-23 | |
| dc.date.accessioned | 2026-07-07T04:39:47Z | |
| dc.date.available | 2026-07-07T04:39:47Z | |
| dc.description | In this paper we investigate three unsolved conjectures in geometric combinatorics, namely Falconer's distance set conjecture, the dimension of Furstenburg sets, and Erdos's ring conjecture. We formulate natural $δ$-discretized versions of these conjectures and show that in a certain sense that these discretized versions are equivalent. In particular, it appears that to progress on any of these problems one must prove a quantitative statement about the existence of sub-rings of $R$ of dimension 1/2. | |
| dc.description | 42 pages, 5 figures, submitted, New York Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0101195 | |
| dc.identifier | http://arxiv.org/abs/math/0101195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60807 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 05B99; 28A78; 28A75 | |
| dc.title | Some connections between Falconer's distance set conjecture, and sets of Furstenburg type | |
| dc.type | text |