Blow-up in non homogeneous Lie groups and rectifiability,

In this paper we extend the De Giorgi notion of rectifiability of surfaces in non homogeneous Lie groups. This notion and the principal properties of Cacciopoli sets had already been proved in homogeneous Lie group, using a blow-up method, with respect to the natural dilations. In non homogeneous Lie groups no dilations are defined, so that we need to apply a freezing method, locally approximating the non homogeneous structure, with an homogeneous one.