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# Existence of isoperimetric regions in sub-Finsler nilpotent groups

We consider a nilpotent Lie group with a bracket-generating distribution $$\mathcal{H}$$ and an asymmetric left-invariant norm $$\|\cdot\|_K$$ induced by a convex body $$K\subseteq\mathcal{H}_0$$ containing $$0$$ in its interior. In this talk, we will associate a left-invariant perimeter functional $$P_K$$ to $$K$$ following De Giorgi's definition of perimeter and prove the existence of minimizers of $$P_K$$ under a volume (Haar measure) constraint. We will also discuss some properties of the isoperimetric regions and the isoperimetric profile.