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math.AP2009★ 3 cited
Isoperimetric, Sobolev and Poincaré inequalities on hypersurfaces in sub-Riemannian Carnot groups
F. Montefalcone
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Among other results, we shall prove an isoperimetric inequality for…
math.AP2009★ 7 cited
CC-distance and metric normal of smooth hypersurfaces in sub-Riemannian Carnot groups
N. Arcozzi, F. Ferrari, F. Montefalcone
In this paper we study the main geometric properties of the Carnot-Carathéodory (abbreviated CC) distance $\dc$ in the setting of -step sub-Riemannian Carnot groups from many di…