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

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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 languageEnglish
Pages (from-to)1075-1105
JournalIndiana University Mathematics Journal
Volume54
DOIs
Publication statusPublished - 17 Oct 2005

Keywords

  • Analytic capacity
  • Curvature of measures
  • Rectifiability

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