Szemer\'edi-Trotter bounds for tubes and applications
Ciprian Demeter, Hong Wang
TL;DR
This paper establishes precise incidence bounds for planar tubes under packing conditions and applies these results to enhance Fourier transform estimates of fractal measures on curves.
Contribution
It introduces sharp incidence bounds for tubes with packing constraints and leverages them to improve Fourier analysis of fractal measures on curves.
Findings
Improved incidence bounds for planar tubes.
Enhanced Fourier transform estimates for fractal measures.
Applications to geometric measure theory.
Abstract
We prove sharp estimates for incidences involving planar tubes that satisfy packing conditions. We apply them to improve the estimates for the Fourier transform of fractal measures supported on planar curves.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Nonlinear Partial Differential Equations