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.
Random constructions for sharp estimates of mizohata-takeuchi type
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.CA 2years
2026 2representative citing papers
Constructs lattice point sets with many rectangles and few isosceles triangles to produce explicit counterexamples to the Mizohata-Takeuchi conjecture for the paraboloid via transference principles.
citing papers explorer
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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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Rectangles, triangles and Schr\"{o}dinger waves
Constructs lattice point sets with many rectangles and few isosceles triangles to produce explicit counterexamples to the Mizohata-Takeuchi conjecture for the paraboloid via transference principles.