On the classification of complete area-stationary and stable surfaces in the subriemannian Sol manifold

e study the classification of area-stationary and stable C2 regular surfaces in the space of the rigid motions of the Minkowski plane E(1, 1), equipped with its subriemannian structure. We construct examples of area-stationary surfaces that are not foliated by subriemannian geodesics. We also prove that there exist an infinite number of C2 area-stationary surfaces with a singular curve. Finally we show the stability of C2 area-stationary surfaces foliated by subriemannian geodesics.