Kakeya sets over non-archimedean local rings

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.

10 pages

Cited by in corpus (2)

• Kakeya-Type Sets in Local Fields with Finite Residue Field
• Variants of the Kakeya problem over an algebraically closed field