Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 357-365

SOME REMARKS ON DENSITIES IN THE HEISENBERG GROUP

Valentino Magnani

Università di Pisa, Dipartimento di Matematica
Largo Pontecorvo 5, I-56127 Pisa, Italy; magnani 'at' dm.unipi.it

Abstract. 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.

2010 Mathematics Subject Classification: Primary 28A75; Secondary 53C17, 22E30.

Key words: Heisenberg group, Hausdorff measure, density, rectifiability.

Reference to this article: V. Magnani: Some remarks on densities in the Heisenberg group. Ann. Acad. Sci. Fenn. Math. 42 (2017), 357-365.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4217