Falconer distance problem on Riemannian manifolds

Fuente: arXiv
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Main Authors: Jian, Changbiao, Liu, Bochen, Xi, Yakun
Format: Preprint
Published: 2023
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author Jian, Changbiao
Liu, Bochen
Xi, Yakun
author_facet Jian, Changbiao
Liu, Bochen
Xi, Yakun
contents We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$
format Preprint
id arxiv_https___arxiv_org_abs_2309_01204
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Falconer distance problem on Riemannian manifolds
Jian, Changbiao
Liu, Bochen
Xi, Yakun
Classical Analysis and ODEs
Analysis of PDEs
We prove that on a $d$-dimensional Riemannian manifold, the distance set of a Borel set $E$ has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)^d}{8d}.$$
title Falconer distance problem on Riemannian manifolds
topic Classical Analysis and ODEs
Analysis of PDEs
url https://arxiv.org/abs/2309.01204