Maximal surfaces in anti-de Sitter 3-manifolds with particles (Q507071)

A \textit{particle} in an anti-de Sitter globally hyperbolic maximal (AdS GHM) manifold is a conical singularity along a time-like line. A main result of the paper under review is the following. Theorem 1.4: For each AdS convex GHM \(3\)-manifold \((M, g)\) with particles of angles less than \(\pi \), there exists a unique maximal space-like surface \(S\hookrightarrow (M, g)\). The obtained picture extends the connections between minimal Lagrangian diffeomorphisms and harmonic maps to the case with conical singularities.