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

الأصل · EN

We 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 sub-Riemannian structure. We construct examples of area-stationary surfaces that are not foliated by sub-Riemannian 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 sub-Riemannian geodesics.