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A note on the
distinct distances problem in the hyperbolic plane
Zhipeng Lu and Xianchang Meng |
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Vol. 327 (2023), No. 1, 129–137
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Abstract |
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We provide a proof of a Guth–Katz-type lower bound for the distinct distances problem in the hyperbolic plane. Our construction follows the framework of Guth and Katz to deal with PSL(R) and the corresponding incidence structure in projective geometry. In addition, we deduce a new sum-product estimate in the form of a hyperbolic metric formula based on this lower bound. |
Keywords
Erdős distinct distances, hyperbolic geometry, sum-product
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Mathematical Subject Classification
Primary: 11P70, 52C10
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Milestones
Received: 4 September 2023
Revised: 19 January 2024
Accepted: 20 January 2024
Published: 18 February 2024
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Authors |
| Zhipeng Lu | |
| Guangdong Laboratory of Machine
Perception and Intelligent Computing Department of Engineering Shenzhen MSU-BIT University Shenzhen China |
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| Xianchang Meng | |
| School of Mathematics Shandong University Jinan China |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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