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Geometric and Functional Analysis

, Volume 29, Issue 6, pp 1844–1863 | Cite as

Incidence Estimates for Well Spaced Tubes

  • Larry Guth
  • Noam Solomon
  • Hong WangEmail author
Article
  • 59 Downloads

Abstract

We prove analogues of the Szemerédi–Trotter theorem and other incidence theorems using \(\delta \)-tubes in place of straight lines, assuming that the \(\delta \)-tubes are well spaced in a strong sense.

Notes

Acknowledgements

The first author is supported by a Simons Investigator Award. We would like to thank Misha Rudnev for the very nice observation that simplifies the proof of Theorem 1.2. We would like to thank the anonymous referee for a careful reading of the draft and the many helpful suggestions that have improved the exposition of the article. Also, thanks to Yuqiu Fu, Shengwen Gan, Dominique Maldague, and Lingxian Zhang for helpful comments about a draft of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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