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

References in corpus (4)

• Marstrand-Mattila rectifiability criterion for $1$-codimensional measures in Carnot Groups
• Geometry of $1$-codimensional measures in Heisenberg groups
• On uniform measures in the Heisenberg group
• Area of intrinsic graphs and coarea formula in Carnot Groups

Cited by in corpus (5)

• Lipschitz graphs and currents in Heisenberg groups
• Marstrand-Mattila rectifiability criterion for $1$-codimensional measures in Carnot Groups
• Geometry of $1$-codimensional measures in Heisenberg groups
• Rickman rugs and intrinsic bilipschitz graphs
• Unique continuation for locally uniformly distributed measures