On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method
Combinatorics
2025-03-24 v1 Classical Analysis and ODEs
Metric Geometry
Abstract
The Falconer distance problem for Cartesian product sets was introduced and studied by Iosevich and Liu (\cite{MR3525385}). In this paper, by implementing a new observation on Cartesian product sets associated with a particular parabolic structure, we study the pinned version of Falconer distance problem for Cartesian product sets, and improve the threshold for the Falconer distance set in \cite{MR3525385} in certain case.
Cite
@article{arxiv.2503.14108,
title = {On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method},
author = {Ji Li and Chong-Wei Liang and Chun-Yen Shen},
journal= {arXiv preprint arXiv:2503.14108},
year = {2025}
}
Comments
13 pages. Any comment is welcome!!