Incidence theory and restriction estimates
Classical Analysis and ODEs
2014-01-10 v1 Analysis of PDEs
Combinatorics
Abstract
We investigate the interplay between the discrete restriction phenomenon and incidence theory. Two angles are explored. One is a refinement of the machinery developed by Thomas Wolff, which when combined with a recent subcritical estimate of Bourgain leads to new Strichartz estimates for irrational tori. The other one connects various additive energies with the Szemer\'edi-Trotter Theorem. The combination of the two approaches recovers the best known Strichartz estimates for the classical torus in dimensions , without any appeal to number theory.
Cite
@article{arxiv.1401.1873,
title = {Incidence theory and restriction estimates},
author = {Ciprian Demeter},
journal= {arXiv preprint arXiv:1401.1873},
year = {2014}
}