Falconer distance problem on Riemannian manifolds

2023/09/03 by Jian, Changbiao, Liu, Bochen, Xi, Yakun
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.01204

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_H(E)gt;\frac d2+\frac14+(1-(-1)^d)/(8d).

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