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1 results

  • 12 - Incidence Applications in Rd

  • Adam Sheffer, Bernard M. Baruch College, City University of New York
  • Book:
    Polynomial Methods and Incidence Theory
    Published online:
    17 March 2022
    Print publication:
    24 March 2022, pp 172-181

  • 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.