Dimension comparison and H-regular surfaces in Heisenberg groups - Arvila, Miro (2024)
In this thesis we study a specific Carnot group which is the $n$-th Heisenberg group $\mathbb{H}^n = (\mathbb{R}^{2n+1}, *)$. Carnot groups are simply connected nilpotent Lie groups whose Lie algebra admits a stratification. The Heisenberg group $\mathbb{H}^n$ is one of the easiest examples of non-commutative Carnot groups.