A proof of Carleson's $\varepsilon^2$-conjecture
Classical Analysis and ODEs
2019-10-22 v2 Analysis of PDEs
Metric Geometry
Abstract
In this paper we provide a proof of the Carleson -conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson -square function.
Cite
@article{arxiv.1909.08581,
title = {A proof of Carleson's $\varepsilon^2$-conjecture},
author = {Benjamin Jaye and Xavier Tolsa and Michele Villa},
journal= {arXiv preprint arXiv:1909.08581},
year = {2019}
}
Comments
In this version, the proof of Main Lemma 4.2 has been modified so that it does not require the use of the David-Mattila lattice. Several typos have been corrected. Also, Corollary 1.3 is now valid for two-sided corkscrew open sets