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

2010/12/11 by Francescopaolo Montefalcone, Montefalcone, Francescopaolo
Mathematics · #22E60 #46E35 #49Q15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1012.2442

openalex publication_date 2010/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Normal and Integral Currents
• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Related

• Isoperimetric, Sobolev and Poincaré inequalities on hypersurfaces in sub-Riemannian Carnot groups
• Geometric inequalities in Carnot groups
• Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups
• Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in\n Carnot groups
• Stable H-minimal hypersurfaces