*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