AN INCIDENCE RESULT FOR WELL-SPACED ATOMS IN ALL DIMENSIONS

Author:

BRADSHAW PETER J.

Abstract

AbstractWe prove an incidence result counting the k-rich $\delta $ -tubes induced by a well-spaced set of $\delta $ -atoms. Our result coincides with the bound that would be heuristically predicted by the Szemerédi–Trotter theorem and holds in all dimensions $d \geq 2$ . We also prove an analogue of Beck’s theorem for $\delta $ -atoms and $\delta $ -tubes as an application of our result.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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1. How much can heavy lines cover?;Journal of the London Mathematical Society;2024-04-30

2. Incidence estimates for $\alpha$-dimensional tubes and $\beta$-dimensional balls in $\mathbb R^{2}$;Journal of Fractal Geometry, Mathematics of Fractals and Related Topics;2024-04-12

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