A remark on a Bernstein type result for $\hat{I}»$-hypersurfaces

Abstract

We proved that any complete hypersurface in the Euclidean space ${\mathbb{R}}^{n+1}$ whose Gauss image is contained in an open hemisphere has to be proper. As applications, we derive a counterpart of Hoffman-Osserman-Schoen's result for $\hat{I}»$-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \cite{CW14b}.

There is an error in the proof of the main theorem