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.
A counterexample to the mizohata-takeuchi conjecture
3 Pith papers cite this work. Polarity classification is still indexing.
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2026 3verdicts
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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.
Under dim_H E >1, dim_H E + dim_H F >2 and F regular (equal Hausdorff and packing dimensions), there exists y in F such that the pinned distance set Δ_y(E) has positive Lebesgue measure.
citing papers explorer
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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.
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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.
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Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
Under dim_H E >1, dim_H E + dim_H F >2 and F regular (equal Hausdorff and packing dimensions), there exists y in F such that the pinned distance set Δ_y(E) has positive Lebesgue measure.