Evolution of spacelike surfaces in AdS 3 by their Lagrangian angle

We study spacelike hypersurfaces M in an anti-De Sitter spacetime N of constant sectional curvature − κ, κ > 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 ⊂ N and the sectional curvature of N satisfy | K | < κ .

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