A proof of Carleson’s \(\varepsilon^2\)-conjecture. (English) Zbl 1472.28005

Summary: In this paper we provide a proof of the Carleson \(\varepsilon^2\)-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 \(\varepsilon^2\)-square function.


28A75 Length, area, volume, other geometric measure theory
28A78 Hausdorff and packing measures
30C85 Capacity and harmonic measure in the complex plane
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