On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913749247459328 |
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| author | Li, Ji Liang, Chong-Wei Shen, Chun-Yen |
| author_facet | Li, Ji Liang, Chong-Wei Shen, Chun-Yen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_14108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method Li, Ji Liang, Chong-Wei Shen, Chun-Yen Combinatorics Classical Analysis and ODEs Metric Geometry 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. |
| title | On Pinned Falconer Distance Problem for Cartesian Product Sets: the Parabolic Method |
| topic | Combinatorics Classical Analysis and ODEs Metric Geometry |
| url | https://arxiv.org/abs/2503.14108 |