Existence of maximal surface containing given curve and special   singularity
  We give a different formulation for describing maximal surfaces in Lorentz-Minkowski space, $\mathbb{L}^3$, using the identification of $\mathbb L^3$ with $\mathbb C\times \mathbb R$. Further we give a different proof for the singular Bj\"orling problem for the case of closed real analytic null curve. As an application, we show the existence of maximal surface which contains a given curve and has a special singularity. 
Rukmini Dey, Pradip Kumar, and Rahul Kumar Singh
math.DG math.CV