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

Isabel Fernandez·Francisco J. Lopez
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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.

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Isabel Fernandez, Francisco J. Lopez. 2004-10-20. Relative parabolicity of zero mean curvature surfaces in $R^3$ and $R_1^3$. https://arxiv.org/abs/math/0410435

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