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math.CA2024
Orthogonal projection, dual Furstenberg problem, and discretized sum-product
Longhui Li, Bochen Liu
In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via estimates of orthogonal projections. Examples are also discussed. Moreo…
math.CA2024
Falconer distance problem on Riemannian manifolds
Changbiao Jian, Bochen Liu, Yakun Xi
We prove that on a -dimensional Riemannian manifold, the distance set of a Borel set has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)…