Existence of maximal surface containing given curve and special singularity

Abstract

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 Björling 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.

15 pages, Additional affiliation added