Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups

Abstract

In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups. In this case, we will prove the convex hull property and some “exclosure theorems” for H-minimal hypersurfaces of class C2 satisfying a Hörmander-type condition.

Keywords

• carnot groups
• sub-riemannian geometry
• h-minimal hypersurfaces
• convex hull property
• exclosure theorems