English

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 ε2\varepsilon^2-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 ε2\varepsilon^2-square function.

Keywords

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