[LIBRO][B] An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem

L Capogna, D Danielli, SD Pauls, J Tyson - 2007 - books.google.com
This book gives an up-to-date account of progress on Pansu's celebrated problem on the
sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an …

Size of characteristic sets and functions with prescribed gradient

ZM Balogh - 2003 - degruyter.com
The characteristic set CšSŽ of a codimension 1 submanifold S in the Heisenberg group Hn
consists of those points where the tangent space of S coincides with the space spanned by …

[PDF][PDF] Some topics of geometric measure theory in Carnot groups

FS Cassano - Geometry, analysis and dynamics on sub …, 2016 - researchgate.net
These notes aim at illustrating some results achieved in the geometric measure theory in
Carnot groups. They are an extended version of a part of the course Geometric Measure …

Intrinsic regular hypersurfaces in Heisenberg groups

L Ambrosio, FS Cassano, D Vittone - The Journal of Geometric Analysis, 2006 - Springer
We study the ℍ-regular surfaces, a class of intrinsic regular hypersurfaces in the setting of
the Heisenberg group ℍ n= ℂ n× ℝ= ℝ 2n+ 1 endowed with a leftinvariant metric d∞ …

Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

B Kirchheim, F Serra Cassano - … Normale Superiore di Pisa-Classe di …, 2004 - numdam.org
Rectifiability and Parameterization of Intrinsic Regular Surfaces in the Heisenberg Group Page
1 Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. III (2004), pp. 871-896 Rectifiability and …

The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

VB Adesi, FS Cassano, D Vittone - Calculus of Variations and Partial …, 2007 - Springer
In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-
Carathéodory (CC) structures. More precisely we will introduce a general calibration method …

On the Hausdorff volume in sub-Riemannian geometry

A Agrachev, D Barilari, U Boscain - Calculus of Variations and Partial …, 2012 - Springer
For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the
spherical Hausdorff measure with respect to a smooth volume. We prove that this is the …

Characterizations of intrinsic rectifiability in Heisenberg groups

P Mattila, R Serapioni, F Serra Cassano - Annali della Scuola Normale …, 2010 - numdam.org
We define rectifiable sets in the Heisenberg groups as countable unions of Lipschitz images
of subsets of a Euclidean space, in the case of lowdimensional sets, or as countable unions …

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups

ZM Balogh, JT Tyson, B Warhurst - Advances in mathematics, 2009 - Elsevier
We solve Gromov's dimension comparison problem for Hausdorff and box counting
dimension on Carnot groups equipped with a Carnot–Carathéodory metric and an adapted …

[HTML][HTML] Projection and slicing theorems in Heisenberg groups

ZM Balogh, K Fässler, P Mattila, JT Tyson - Advances in mathematics, 2012 - Elsevier
We study the behavior of the Hausdorff dimension of sets in the Heisenberg group Hn, n∈
N, with a sub-Riemannian metric under projections onto horizontal and vertical subgroups …