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 C2-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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