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The $p$-adic Kakeya conjecture (2108.03750v3)
Published 8 Aug 2021 in math.NT, math.CA, and math.MG
Abstract: We prove that all bounded subsets of $\mathbb{Q}_pn$ containing a line segment of unit length in every direction have Hausdorff and Minkowski dimension $n$. This is the analogue of the classical Kakeya conjecture with $\mathbb{R}$ replaced by $\mathbb{Q}_p$.
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