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arXiv · 2309.01204

Falconer distance problem on Riemannian manifolds

Changbiao Jian·Bochen Liu·Yakun Xi
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Abstract

We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$

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Changbiao Jian, Bochen Liu, Yakun Xi. 2023-09-03. Falconer distance problem on Riemannian manifolds. https://arxiv.org/abs/2309.01204

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