Incidence Estimates for Well Spaced Tubes

By Larry Guth, Noam Solomon, Hong Wang. Geometric and Functional Analysis, 2019

56 citations recorded by the source corpus.

We prove analogues of the Szemerédi–Trotter theorem and other incidence theorems using δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}-tubes in place of straight lines, assuming that the δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}-tubes are well spaced in a strong sense.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bbe8a3268ce8e84ea8b3b52db634dd2e9d1ea67f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Hong Wang
2. Larry Guth
3. Pablo Shmerkin
4. Tuomas Orponen
5. Noam Solomon
6. Jonathan M. Fraser
7. Tamás Keleti

In Geometry and Topology

1. Hong Wang
2. Ruixiang Zhang
3. Pablo Shmerkin
4. Larry Guth
5. Tuomas Orponen
6. F. C. Marques
7. A. Neves
8. F. Schlenk

In Mathematical Physics

1. Hong Wang
2. Ruixiang Zhang
3. Larry Guth
4. Pablo Shmerkin
5. Tuomas Orponen
6. Xiumin Du
7. Meng Wu
8. P. P. Varj'u

Citations in the corpus

• A sharp square function estimate for the cone in ℝ3 (2019, background): “It builds on [14], which applies similar ideas to rectangles and tubes instead of planks.”
• On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021, background): “Wang [8] proved incidence theorems for "well spaced" tubes.”