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arXiv · 2107.11937

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

Yuqiu Fu·Shengwen Gan·Kevin Ren
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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.

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Yuqiu Fu, Shengwen Gan, Kevin Ren. 2021-07-26. An incidence estimate and a Furstenberg type estimate for tubes in $\mathbb{R}^2$. https://arxiv.org/abs/2107.11937

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