Antonio Córdoba

Curly Kakeya: The Hausdorff dimension of sets containing circles or line segments in many directions

In this paper, we establish a lower bound for the Hausdorff dimension of a set 𝐾 ⊂ ℝ 𝑛 that contains a dilated and translated copy of every meridian, that is, of every ( 𝑑 − 2 ) -dimensional sphere passing through the poles of 𝑆 𝑑 − 1 , a ( 𝑑 − 1 ) -dimensional sphere, with 3 ≤ 𝑑...