Relative parabolicity of zero mean curvature surfaces in R3 and R13
Isabel Fernandez, Francisco J. Lopez
Abstract
If the Lorentzian norm on a maximal surface in the 3-dimensional Lorentz-Minkowski space R13 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 R13 and R3, respectively, are relative parabolic.
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