Existence of isoperimetric regions in sub-Finsler nilpotent groups

Abstract

We consider a nilpotent Lie group with a bracket-generating distribution ℋ{\mathcal{ {\mathcal H} }} and an asymmetric left-invariant norm ∣⋅∣K{| \cdot | }_{K} induced by a convex body K⊆RkK\subseteq {{\mathbb{R}}}^{k} containing 0 in its interior. In this study, we prove the existence of minimizers of the perimeter functional PK{P}_{K} associated with ∣⋅∣K{| \cdot | }_{K} under a volume (Haar measure) constraint.

Keywords

• isoperimetric regions
• nilpotent lie groups
• sub-riemannian geometry
• 53c17
• 49q20