Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space

Abstract

Calabi and Cheng-Yau's Bernstein-type theorem asserts that an entire zero mean curvature graph in Lorentz-Minkowski $(n+1)$-space ${\mathbf{R}}_1^{n+1}$ which admits only space-like points is a hyperplane. Recently, the third and fourth authors proved a line theorem for hypersurfaces at their degenerate light-like points. Using this, we give an improvement of the Bernstein-type theorem, and we show that an entire zero mean curvature graph in ${\mathbf{R}}_1^{n+1}$ consisting only of space-like or light-like points is a hyperplane. This is a generalization of the first, third and fourth authors' previous result for $n=2$.

4 pages; Metadata are updated on July 20

References in corpus (1)

• Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality