OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Resolves the Falconer distance conjecture in every dimension d ≥ 2: every compact set E\subset\mathbb R^d with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue measure.
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We resolve the Falconer distance conjecture in every dimension. For every integer d ≥ 2, a compact subset of ℝ^(d) with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue measure.
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