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.
A counterexample to the mizohata-takeuchi conjecture
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
years
2026 3representative 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.
New logarithm laws and lattice point bounds yield a proof of power loss in the Mizohata-Takeuchi conjecture with explicit errors and establish genericity in C^k.
citing papers explorer
-
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.
-
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.
-
Cusp Excursions, Lattice Points on Manifolds, and the Mizohata-Takeuchi Conjecture
New logarithm laws and lattice point bounds yield a proof of power loss in the Mizohata-Takeuchi conjecture with explicit errors and establish genericity in C^k.