Existence of isoperimetric regions in contact sub-Riemannian manifolds

Abstract

We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Riemannian metric is compact.

24 pages, no figures

References in corpus (2)

• The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
• Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group H^n

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• Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies
• Stable minimal graphs in Heisenberg group ${\mathbb{H}}^n$
• Existence, characterization and stability of Pansu spheres in sub-Riemannian $3$-space forms