Incidences between points and circles in three and higher dimensions

  title={Incidences between points and circles in three and higher dimensions},
  author={Boris Aronov and Vladlen Koltun and Micha Sharir},
  booktitle={SCG '02},
(MATH) We show that the number of incidences between <i>m</i> distinct points and <i>n</i> distinct circles in $\reals^3$ is <i>O</i>(<i>m</i> <sup>4/7</sup> <i>n</i> <sup>17/21</sup>+<i>m</i> <sup>2/3</sup> <i>n</i> <sup>2/3</sup>+<i>m</i>+<i>n</i>); the bound is optimal for <i>m n</i> <sup>3/2</sup>. This result extends recent work on point-circle incidences in the plane, but its proof requires a different analysis. The bound improves upon a previous bound, noted by Akutsu et al. [2] and by… 

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