Finite Curvature of Arc Length Measure Implies Rectifiability: a New Proof
نویسنده
چکیده
If E ⊂ C is a set with finite length and finite curvature, then E is rectifiable. This fact, proved by David and Léger 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.
منابع مشابه
THE WEAK-A∞ PROPERTY OF HARMONIC AND p-HARMONIC MEASURES IMPLIES UNIFORM RECTIFIABILITY
Let E ⊂ Rn+1, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞ property of harmonic measure, for the open set Ω := Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < ∞.
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