Parabolicity of maximal surfaces in Lorentzian product spaces |
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Authors: | Alma L Albujer Luis J Alías |
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Institution: | 1. Departamento de Matemáticas, Universidad de Murcia, 30100, Espinardo, Murcia, Spain
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Abstract: | In this paper we establish some parabolicity criteria for maximal surfaces immersed into a Lorentzian product space of the form ${M^2 \times \mathbb {R}_1}$ , where M 2 is a connected Riemannian surface with non-negative Gaussian curvature and ${M^2 \times \mathbb {R}_1}$ is endowed with the Lorentzian product metric ${{\langle , \rangle}={\langle , \rangle}_M-dt^2}$ . In particular, and as an application of our main result, we deduce that every maximal graph over a starlike domain ${\Omega \subseteq M}$ is parabolic. This allows us to give an alternative proof of the non-parametric version of the Calabi–Bernstein result for entire maximal graphs in ${M^2 \times \mathbb {R}_1}$ . |
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