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arXiv · 1012.2442

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

Francescopaolo Montefalcone
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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.

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BibTeXRIS

Francescopaolo Montefalcone. 2010-12-11. Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups. https://arxiv.org/abs/1012.2442

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