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arXiv · 2103.06630

Existence of isoperimetric regions in sub-Finsler nilpotent groups

Julián Pozuelo
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Abstract

We consider a nilpotent Lie group with a bracket-generating distribution $\hhh$ and an asymmetric left-invariant norm $\|\cdot\|_K$ induced by a convex body $K\subseteq\hhh$ containing $0$ in its interior. In this paper we prove the existence of minimizers of the perimeter functional $P_K$ associated to $\|\cdot\|_K$ under a volume (Haar measure) constraint. Our result generalizes the one of Leonardi and Rigot for Carnot groups.

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Julián Pozuelo. 2021-03-11. Existence of isoperimetric regions in sub-Finsler nilpotent groups. https://arxiv.org/abs/2103.06630

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