Relative parabolicity of zero mean curvature surfaces in $R^3$ and   $R_1^3$
  If the Lorentzian norm on a maximal surface in the 3-dimensional Lorentz-Minkowski space $R_1^3$ is positive and proper, then the surface is relative parabolic. As a consequence, entire maximal graphs with a closed set of isolated singularities are relative parabolic.   Furthermore, maximal and minimal graphs over closed starlike domains in $R_1^3$ and $R^3,$ respectively, are relative parabolic. 
Isabel Fernandez and Francisco J. Lopez