Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Differential Geometry
2012-12-17 v6
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.
Keywords
Cite
@article{arxiv.1012.2442,
title = {Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups},
author = {Francescopaolo Montefalcone},
journal= {arXiv preprint arXiv:1012.2442},
year = {2012}
}
Comments
43 pages. arXiv admin note: text overlap with arXiv:0910.5656