Finite curvature of arc length measure implies rectifiability: a new proof
Xavier Tolsa
30C8528A75curvature of measuresrectifiabilityanalytic capacity
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.
Indiana University Mathematics Journal
2005
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10.1512/iumj.2005.54.2746
10.1512/iumj.2005.54.2746
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Indiana Univ. Math. J. 54 (2005) 1075 - 1106
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