Algebraic Methods in Discrete Analogs of the Kakeya Problem
| dc.creator | Guth, Larry | |
| dc.creator | Katz, Nets Hawk | |
| dc.date | 2008-12-04 | |
| dc.date.accessioned | 2026-07-07T12:09:45Z | |
| dc.date.available | 2026-07-07T12:09:45Z | |
| dc.description | We prove the joints conjecture, showing that for any $N$ lines in ${\Bbb R}^3$, there are at most $O(N^{3 \over 2})$ points at which 3 lines intersect non-coplanarly. We also prove a conjecture of Bourgain showing that given $N^2$ lines in ${\Bbb R}^3$ so that no $N$ lines lie in the same plane and so that each line intersects a set $P$ of points in at least $N$ points then the cardinality of the set of points is $Ω(N^3)$. Both our proofs are adaptations of Dvir's argument for the finite field Kakeya problem. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0812.1043 | |
| dc.identifier | http://arxiv.org/abs/0812.1043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209732 | |
| dc.subject | Combinatorics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 52C10; 14A25 | |
| dc.title | Algebraic Methods in Discrete Analogs of the Kakeya Problem | |
| dc.type | text |