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.
Weighted refined decoupling estimates and application to falconer distance set problem
2 Pith papers cite this work. Polarity classification is still indexing.
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math.CA 2years
2026 2representative citing papers
Extends the sharp dimensional threshold k from d=k+1 to the range k+1 ≤ d ≤ 2k and gives a non-trivial threshold of d-k for d > 2k in the simplex volume problem.
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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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On volumes of simplices in intermediate dimensions
Extends the sharp dimensional threshold k from d=k+1 to the range k+1 ≤ d ≤ 2k and gives a non-trivial threshold of d-k for d > 2k in the simplex volume problem.