English

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

Differential Geometry 2019-11-11 v2

Abstract

We proved that any complete hypersurface in the Euclidean space Rn+1\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 λ\lambda-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \cite{CW14b}.

Keywords

Cite

@article{arxiv.1910.11175,
  title  = {A remark on a Bernstein type result for $\lambda$-hypersurfaces},
  author = {Hongbing Qiu and Linlin Sun},
  journal= {arXiv preprint arXiv:1910.11175},
  year   = {2019}
}

Comments

There is an error in the proof of the main theorem

R2 v1 2026-06-23T11:53:49.611Z