Kakeya sets over non-archimedean local rings
Combinatorics
2014-01-14 v1
Abstract
In a recent paper of Ellenberg, Oberlin, and Tao, the authors asked whether there are Besicovitch phenomena in F_q[[t]]^n. In this paper, we answer their question in the affirmative by explicitly constructing a Kakeya set in F_q[[t]]^n of measure 0. Furthermore, we prove that any Kakeya set in F_q[[t]]^2 or Z_p^2 is of Minkowski dimension 2.
Cite
@article{arxiv.1112.3381,
title = {Kakeya sets over non-archimedean local rings},
author = {Evan P. Dummit and Márton Hablicsek},
journal= {arXiv preprint arXiv:1112.3381},
year = {2014}
}
Comments
10 pages