English

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

Differential Geometry 2007-05-23 v1

Abstract

If the Lorentzian norm on a maximal surface in the 3-dimensional Lorentz-Minkowski space R13R_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 R13R_1^3 and R3,R^3, respectively, are relative parabolic.

Keywords

Cite

@article{arxiv.math/0410435,
  title  = {Relative parabolicity of zero mean curvature surfaces in $R^3$ and $R_1^3$},
  author = {Isabel Fernandez and Francisco J. Lopez},
  journal= {arXiv preprint arXiv:math/0410435},
  year   = {2007}
}