The Cauchy problem of Lorentzian minimal surfaces in globally hyperbolic manifolds

In this note a proof is given for global existence and uniqueness of minimal Lorentzian surface maps from a cylinder into a large class of globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives. The results of this article are part of my PhD thesis written at the Max-Planck institute for Mathematics in the Sciences in Leipzig under the supervision of Prof. Jürgen Jost to whom I want to express my gratitude.