Remarks on minimal surfaces in Minkowski space

Stationary surfaces in Lorentzian space may arise as singular limits of the hyperbolic analog of Ginzburg-Landau equations. We describe some qualitative properties of such surfaces, assuming enough regularity. However, singularities may arise. This seems to require a notion of weak solution of the minimal surface equation. We start a discussion on this issue.

Work in collaboraton with Jens Hoppe (KTH, Sweden), Matteo Novaga (Padova, Italy), and Giandomenico Orlandi (Verona, Italy).