Falconer distance problem on Riemannian manifolds
Classical Analysis and ODEs
2024-10-24 v3 Analysis of PDEs
Abstract
We prove that on a -dimensional Riemannian manifold, the distance set of a Borel set has a positive Lebesgue measure if
Keywords
Cite
@article{arxiv.2309.01204,
title = {Falconer distance problem on Riemannian manifolds},
author = {Changbiao Jian and Bochen Liu and Yakun Xi},
journal= {arXiv preprint arXiv:2309.01204},
year = {2024}
}
Comments
18 pages.We have removed the constant sectional curvature condition, which has led to a strengthened version of the main result