Finite curvature of arc length measure implies rectifiability: A new proof

Xavier Tolsa

doi:https://doi.org/10.1512/iumj.2005.54.2746

Finite curvature of arc length measure implies rectifiability: A new proof

Xavier Tolsa

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

Abstract

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. Indiana University Mathematics Journal ©,.

Original language	English
Pages (from-to)	1075-1105
Journal	Indiana University Mathematics Journal
Volume	54
DOIs	https://doi.org/10.1512/iumj.2005.54.2746
Publication status	Published - 17 Oct 2005

Keywords

Analytic capacity
Curvature of measures
Rectifiability

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https://doi.org/10.1512/iumj.2005.54.2746

https://ddd.uab.cat/record/115173

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title = "Finite curvature of arc length measure implies rectifiability: A new proof",

abstract = "If E ⊂ ℂ is a set with finite length and finite curvature, then E is rectifiable. This fact, proved by David and L{\'e}ger 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 {\textcopyright},.",

keywords = "Analytic capacity, Curvature of measures, Rectifiability",

author = "Xavier Tolsa",

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AB - 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. Indiana University Mathematics Journal ©,.

KW - Analytic capacity

KW - Curvature of measures

KW - Rectifiability

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DO - https://doi.org/10.1512/iumj.2005.54.2746

M3 - Article

VL - 54

SP - 1075

EP - 1105

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

ER -

Finite curvature of arc length measure implies rectifiability: A new proof

Abstract

Keywords

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