IUMJ

Title: Finite curvature of arc length measure implies rectifiability: a new proof

Authors: Xavier Tolsa

Issue: Volume 54 (2005), Issue 4, 1075-1106

Abstract:

If $E\subset\mathbb{C}$ is a set with finite length and finite curvature, then $E$ is rectifiable. This fact, proved by David and L\'eger in 1999, is one of the basic ingredients for the proof of Vitushkin's conjecture. In this paper we give another different proof of this result.