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| In this talk we will study the classification of area-stationary and stable $C^2$ regular surfaces in the space of the rigid motions of the Minkowski plane $\mink$, 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 $C^2$ area-stationary surfaces with a singular curve. Finally we show the stability of $C^2$ area-stationary surfaces foliated by sub-Riemannian geodesics. |
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