Calculus of Variations and Geometric Measure Theory

V. Magnani

Some remarks on densities in the Heisenberg group

created by magnani on 15 Sep 2015
modified on 08 Nov 2018


Published Paper

Inserted: 15 sep 2015
Last Updated: 8 nov 2018

Journal: Ann. Acad. Sci. Fenn. Math.
Volume: 42
Number: 1
Pages: 357–365
Year: 2017


We observe that upper densities and spherical Federer densities may differ on all two dimensional surfaces of the sub-Riemannian Heisenberg group. This provides an entire class of intrinsic rectifiable sets having upper density strictly less than one.

Keywords: Hausdorff measure, Heisenberg group, spherical measure, density, rectifiability