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12 - Incidence Applications in Rd

Published online by Cambridge University Press:  17 March 2022

Adam Sheffer
Affiliation:
Bernard M. Baruch College, City University of New York
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Summary

In Chapter 11 we derived general point-variety incidence bounds in R^d. We now study two applications of these bounds. These applications do not require reading any part of Chapter 11, except for the statement of Theorem 11.3. The first application comes from discrete geometry and is another distinct distances problem. Specifically, it is a distinct distances problem with local properties. The second application is a discrete Fourier restriction problem from harmonic analysis. For simplicity, we only discuss the combinatorial aspect of that problem. This aspect is the additive energy of points on a hypersphere.

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Publisher: Cambridge University Press
Print publication year: 2022

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  • Incidence Applications in Rd
  • Adam Sheffer, Bernard M. Baruch College, City University of New York
  • Book: Polynomial Methods and Incidence Theory
  • Online publication: 17 March 2022
  • Chapter DOI: https://doi.org/10.1017/9781108959988.013
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  • Incidence Applications in Rd
  • Adam Sheffer, Bernard M. Baruch College, City University of New York
  • Book: Polynomial Methods and Incidence Theory
  • Online publication: 17 March 2022
  • Chapter DOI: https://doi.org/10.1017/9781108959988.013
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Incidence Applications in Rd
  • Adam Sheffer, Bernard M. Baruch College, City University of New York
  • Book: Polynomial Methods and Incidence Theory
  • Online publication: 17 March 2022
  • Chapter DOI: https://doi.org/10.1017/9781108959988.013
Available formats
×