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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.