Intersection between pencils of tubes, discretized sum-product, and radial projections
Journal
Asian Journal of Mathematics
Journal Volume
27
Journal Issue
6
Start Page
829-852
ISSN
1093-6106
1945-0036
Date Issued
2023
Author(s)
Bochen Liu
Abstract
In this paper we prove the following results in the plane. They are related other, while each of them has its own interest. First we obtain a nontrivial exponent on intersection between pencils of δ-tubes, undconcentration conditions. In fact we show it is equivalent to the discretized sum-product proThen we use our estimates of pencils to prove new results on dimensions of radial projeWe also make a conjecture that would reveal a key difference between orthogonal projectioradial projections.
SDGs
Publisher
International Press of Boston
Type
journal article