Accepted Paper
Inserted: 25 jul 2006
Journal: Boll. Un. Matem. Italiana
Year: 2006
Abstract:
Let $g, t$ be a couple of Lipschitz $*R*^{k+1}$-valued maps defined in an interval $[a,b]$ and such that $Dg=\pm\vert Dg\vert t$ almost everywhere in $[a,b]$. Then $g([a,b])$ is a $C^2$-rectifiable set, namely it may be covered by countably many curves of class $C^2$ embedded in $*R*^{k+1}$. As a consequence, projecting the rectifiable carrier of a one-dimensional generalized Gauss graph provides a $C^2$-rectifiable set.
Keywords: Rectifiable sets, Geometric measure theory, non-homogeneous blow-ups, Whitney extension theorem