For Borel E,F in the plane with dim_H E > 1, dim_H E + dim_H F > 2, and F having equal Hausdorff and packing dimension, some y in F has pinned distance set Delta_y(E) of positive Lebesgue measure.
Stull,Pinned distance sets using effective dimension, arXiv preprint 2207.12501 (2022)
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Sets with optimal oracles satisfy a Kaufman-type bound on the size of exceptional k-plane projections, generalizing Marstrand's theorem via effective descriptive set theory.
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Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
For Borel E,F in the plane with dim_H E > 1, dim_H E + dim_H F > 2, and F having equal Hausdorff and packing dimension, some y in F has pinned distance set Delta_y(E) of positive Lebesgue measure.
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Projections of sets with optimal oracles onto $k$-planes
Sets with optimal oracles satisfy a Kaufman-type bound on the size of exceptional k-plane projections, generalizing Marstrand's theorem via effective descriptive set theory.