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arXiv · 1112.3381

Kakeya sets over non-archimedean local rings

Evan P. Dummit·Márton Hablicsek
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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.

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Evan P. Dummit, Márton Hablicsek. 2011-12-14. Kakeya sets over non-archimedean local rings. https://doi.org/10.1112/s002557931300003x

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