Low dimensional pinned distance sets via spherical averages
Classical Analysis and ODEs
2022-10-11 v2
Abstract
An inequality is derived for the average -energy of pinned distance measures, where . This refines Mattila's theorem on distance sets to pinned distance sets, and gives an analogue of Liu's theorem for pinned distance sets of dimension smaller than 1.
Keywords
Cite
@article{arxiv.2101.12589,
title = {Low dimensional pinned distance sets via spherical averages},
author = {Terence L. J. Harris},
journal= {arXiv preprint arXiv:2101.12589},
year = {2022}
}
Comments
5 pages. Accepted version