A proof of Carleson's ${\epsilon }^2$-conjecture

Abstract

In this paper we provide a proof of the Carleson ${\epsilon }^2$-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 ${\epsilon }^2$-square function.

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