Evolution of spacelike surfaces in \mathrm{AdS}_3 by their Lagrangian angle

We study spacelike hypersurfaces $M$ in an anti-De Sitter spacetime $N$ of constant sectional curvature $-\kappa , \kappa >0$ that evolve by the Lagrangian angle of their Gauß maps. In the two dimensional case we prove a convergence result to a maximal spacelike surface, if the Gauß curvature $K$ of the initial surface $M\subset N$ and the sectional curvature of $N$ satisfy $|K|<\kappa $ .