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.
On the distance sets of self-similar sets.Nonlinearity, 25(6):1919–1929, 2012
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.