English

Geometry of $1$-codimensional measures in Heisenberg groups

Metric Geometry 2021-09-21 v3

Abstract

This paper is devoted to the study of tangential properties of measures with density in the Heisenberg groups Hn\mathbb{H}^n. Among other results we prove that measures with (2n+1)(2n+1)-density have only flat tangents and conclude the classification of uniform measures in H1\mathbb{H}^1.

Keywords

Cite

@article{arxiv.1908.11639,
  title  = {Geometry of $1$-codimensional measures in Heisenberg groups},
  author = {Andrea Merlo},
  journal= {arXiv preprint arXiv:1908.11639},
  year   = {2021}
}

Comments

Correction of typos and very minor details throughout the paper with respect to the published version

R2 v1 2026-06-23T11:00:50.963Z