Bernstein-type theorems for spacelike stationary graphs in Minkowski spaces

Xiang Ma, Peng Wang and Ling Yang

Vol. 287 (2017), No. 1, 159–175

DOI: 10.2140/pjm.2017.287.159

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

Milestones

Received: 7 May 2015

Revised: 2 February 2016

Accepted: 22 July 2016

Published: 6 February 2017