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math.CA2026
Visibility problem in higher dimensions
Yuming He, Changbiao Jian, Yudong Liang
We show that an almost-everywhere upper bound for the Hausdorff dimension of visible parts of all compact planar sets implies the upper bound for visible parts of…
math.CA2023
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)…