Geometric inequalities in Carnot groups
  Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e. codimension one submanifolds) immersed in $\GG$, endowed with the $\HH$-perimeter measure. 
Francescopaolo Montefalcone
math.DG