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distance sets 1harmonic analysis 1Hausdorff dimension 1lebesgue measure 1multi-scale analysis 1pinned distances 1

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math.CA2026

Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates

Bochen Liu

The paper proves that for planar Borel sets with Hausdorff dimensions exceeding certain thresholds, there exists a point in one set whose pinned distance set has positive Lebesgue…