An incidence estimate and a Furstenberg type estimate for tubes in $\mathbb{R}^2$

Yuqiu Fu; Shengwen Gan; Kevin Ren

An incidence estimate and a Furstenberg type estimate for tubes in $\mathbb{R}^2$

Classical Analysis and ODEs 2022-07-05 v2 Combinatorics

Authors: Yuqiu Fu , Shengwen Gan , Kevin Ren

Abstract

We study the $\delta$ -discretized Szemer\'edi-Trotter theorem and Furstenberg set problem. We prove sharp estimates for both two problems assuming tubes satisfy some spacing condition. For both two problems, we construct sharp examples that have many common features.

Keywords

szemerédi-trotter theorem furstenberg set problem tube incidence spacing condition discretized estimate sharp examples

Cite

@article{arxiv.2107.11937,
  title  = {An incidence estimate and a Furstenberg type estimate for tubes in $\mathbb{R}^2$},
  author = {Yuqiu Fu and Shengwen Gan and Kevin Ren},
  journal= {arXiv preprint arXiv:2107.11937},
  year   = {2022}
}

Comments

23 pages; to appear in Journal of Fourier Analysis and Applications

An incidence estimate and a Furstenberg type estimate for tubes in $\mathbb{R}^2$

Abstract

Keywords

Cite

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