Non-Euclidean isoperimetric inequalities for nilpotent Lie groups
Metric Geometry
2019-02-15 v1
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.
Keywords
Cite
@article{arxiv.1902.05469,
title = {Non-Euclidean isoperimetric inequalities for nilpotent Lie groups},
author = {Moritz Gruber},
journal= {arXiv preprint arXiv:1902.05469},
year = {2019}
}
Comments
9 pages