Vol. 287, No. 1, 2017

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Bernstein-type theorems for spacelike stationary graphs in Minkowski spaces

Xiang Ma, Peng Wang and Ling Yang

Vol. 287 (2017), No. 1, 159–175
Abstract

For entire spacelike stationary 2-dimensional graphs in Minkowski spaces, we establish Bernstein-type theorems under specific boundedness assumptions either on the $W$-function or on the total (Gaussian) curvature. These conclusions imply the classical Bernstein theorem for minimal surfaces in ${ℝ}^{3}$ and Calabi’s theorem for spacelike maximal surfaces in ${ℝ}_{1}^{3}$.

Keywords
Bernstein problems, spacelike, stationary, entire graph
Mathematical Subject Classification 2010
Primary: 30F15, 53C24, 58J05