Mathematics > Combinatorics
[Submitted on 18 Mar 2025
]
Title: On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method
Title: 关于笛卡尔乘积集的固定Falconer距离问题：抛物线方法
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.
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