English

Low dimensional pinned distance sets via spherical averages

Classical Analysis and ODEs 2022-10-11 v2

Abstract

An inequality is derived for the average tt-energy of pinned distance measures, where 0<t<10 < t < 1. 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

R2 v1 2026-06-23T22:39:24.526Z