Geometry of $1$-codimensional measures in Heisenberg groups

Abstract

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

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