Geometric inequalities in Carnot groups

Abstract

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.Comment: 26 page