Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space

Abstract

There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in $\mathbb{I}^3$, which implies a Bernstein-type theorem for CMC $H$ graphs in $\mathbb{I}^3$.