A remark on a Bernstein type result for $\lambda$-hypersurfaces

Hongbing Qiu; Linlin Sun

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arXiv · 1910.11175

A remark on a Bernstein type result for $\lambda$-hypersurfaces

Hongbing Qiu·Linlin Sun

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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 $\lambda$-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \cite{CW14b}.

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Hongbing Qiu, Linlin Sun. 2019-10-24. A remark on a Bernstein type result for $\lambda$-hypersurfaces. https://arxiv.org/abs/1910.11175

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