Inserted: 6 jul 2005
Last Updated: 25 jul 2006
Journal: Pacific J. Math.
Let $ \gamma_0 $ be a Lipschitz curve. Our main result provides a sufficient condition, expressed in terms of further accessory Lipschitz maps, for the $C^3$-rectifiability of the image of $\gamma_0$. Such a condition finds a natural interpretation in the context of Gauss maps of curves and in fact an application to one-dimensional generalized Gauss graphs is given.
Keywords: Rectifiable sets, Whitney extension theorem