Relative parabolicity of zero mean curvature surfaces in $R^3$ and $R_1^3$

Abstract

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.

References in corpus (1)

• The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space ${ł}^3$