Area-stationary and stable surfaces of class $C^1$ in the sub-Riemannian Heisenberg group ${\mathbb{H}}^1$

Matteo Galli, Manuel Ritoré

We consider surfaces of class $C^1$ in the $3$-dimensional sub-Riemannian Heisenberg group ${\mathbb{H}}^1$. Assuming the surface is area-stationary, i.e., a critical point of the s…