2019/10/24 by Hongbing Qiu, Qiu, Hongbing, Linlin Sun +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG
paper · pdf · doi:10.48550/arxiv.1910.11175
There is an error in the proof of the main theorem
openalex publication_date 2019/10/24 · openalex created_date 2019/11/01 · arxiv created 2019/11/08 · arxiv updated 2019/11/11 · openalex updated_date 2026/07/28
We proved that any complete hypersurface in the Euclidean space ℝn+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-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \citeCW14b.