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

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

2004-10-20

arxiv.org/abs/math/0410435v1

Mathematics

Differential Geometry

Scientific paper

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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