Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups

Abstract

Let G be a k-step Carnot group. We prove an isoperimetric-type inequality for compact C^2-smooth immersed hypersurfaces with boundary, involving the horizontal mean curvature of the hypersurface. This generalizes an inequality due to Michael and Simon, and Allard, independently. Some applications are discussed.

43 pages. arXiv admin note: text overlap with arXiv:0910.5656

References in corpus (2)

• The Bernstein Problem in the Heisenberg Group
• Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups $H^n,n>1$

Cited by in corpus (2)

• First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds
• Intrinsic complements of equiregular sub-Riemannian manifolds