A result about C³-rectifiability of Lipschitz curves

Silvano Delladio

Vol. 230 (2007), No. 2, 257–270

DOI: 10.2140/pjm.2007.230.257

Abstract

Let γ₀ : [a,b] → ℝ^1+k be Lipschitz. Our main result provides a sufficient condition, expressed in terms of further accessory Lipschitz maps, for the C³-rectifiability of γ₀([a,b]).

Keywords

rectifiable sets, geometric measure theory, Whitney extension theorem

Mathematical Subject Classification 2000

Primary: 49Q15, 53A04

Secondary: 26A12, 26A16, 28A75, 28A78, 54C20

Milestones

Received: 18 August 2005

Accepted: 18 May 2006

Published: 1 April 2007