3 papers
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.AP2025
Sharp spectral-cluster restriction bounds for orthonormal systems
Changbiao Jian, Xing Wang, Yakun Xi
Let be a smooth submanifold of a compact Riemannian manifold . We study the restriction to of densities generated by -orthonormal systems of eigenfunctions whose…
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)…