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.
Spherical averages of Fourier transforms of measures with finite energy; dimension of intersections and distance sets.Mathematika, 34(2):207–228
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
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.