A chord-arc covering theorem in Hilbert space

2009/05/27 by Jonas Azzam, Azzam, Jonas
Mathematics · #28A75 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Metric Geometry (math.MG) #math.CA #math.MG #msc:28A75

paper · pdf · doi:10.48550/arxiv.0905.4317

Withdrawn due to an error

openalex publication_date 2009/05/27 · arxiv created 2011/06/21 · arxiv updated 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there exists M>0 such that for any closed rectifiable curve Γ in Hilbert space, almost every point in Γ is contained in a countable union of M chord-arc curves whose total length is no more than M times the length of Γ.

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