Bernstein type theorems for spacelike stationary graphs in Minkowski spaces

TL;DR

This paper proves Bernstein type theorems for spacelike stationary graphs in Minkowski spaces, extending classical results for minimal and maximal surfaces under certain boundedness conditions.

Contribution

It establishes new Bernstein type theorems for spacelike stationary graphs in Minkowski spaces, generalizing classical minimal surface results.

Findings

Bernstein type theorems are valid under boundedness assumptions on the W-function or total curvature.

Classical Bernstein and Calabi's theorems are recovered as special cases.

Results apply to entire spacelike stationary 2D graphs in Minkowski spaces.

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 3-dimensional Euclidean space and Calabi's theorem for spacelike maximal surfaces in 3-dimensional Minkowski space.