arxiv:2502.17655

Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions

Published on Feb 24

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Abstract

We study sets of delta tubes in R^3, with the property that not too many tubes can be contained inside a common convex set V. We show that the union of tubes from such a set must have almost maximal volume. As a consequence, we prove that every Kakeya set in R^3 has Minkowski and Hausdorff dimension 3.

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