Kakeya-Type Sets in Local Fields with Finite Residue Field

Abstract

We present a construction of a measure-zero Kakeya-type set in a finite-dimensional space $K^d$ over a local field with finite residue field. The construction is an adaptation of the ideas appearing in [12] and [13]. The existence of measure-zero Kakeya-type sets over discrete valuation rings is also discussed, giving an alternative construction to the one presented in [4] over ${\mathbb{F}}_q[[t]]$.

15 pages

References in corpus (1)

• Kakeya sets over non-archimedean local rings

Cited by in corpus (2)

• Proof of the Kakeya set conjecture over rings of integers modulo square-free $N$
• The Kakeya Set Conjecture for $\mathbb{Z}/N\mathbb{Z}$ for general $N$