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This article treats isoperimetric inequalities for integral currents in thesetting of stratified nilpotent Lie groups equipped with left-invariantRiemannian metrics. We prove that for each such group there is a dimension inwhich no Euclidean isoperimetric inequality is admitted, while in all smallerdimensions strictly Euclidean isoperimetric inequalities are satisfied.

Non-Euclidean isoperimetric inequalities for nilpotent Lie groups