Non-Euclidean isoperimetric inequalities for nilpotent Lie groups

2019/02/14 by Moritz Gruber, Gruber, Moritz
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.05469

openalex publication_date 2019/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article treats isoperimetric inequalities for integral currents in the setting of stratified nilpotent Lie groups equipped with left-invariant Riemannian metrics. We prove that for each such group there is a dimension in which no Euclidean isoperimetric inequality is admitted, while in all smaller dimensions strictly Euclidean isoperimetric inequalities are satisfied.

Citations

• Normal and Integral Currents

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