Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature
Differential Geometry
2026-01-14 v1 Analysis of PDEs
Abstract
In this paper, we prove Bernstein type theorems for entire convex graphical hypersurfaces with zero Gaussian curvature in both Euclidean and Minkowski context. A supplementary example illustrates that zero Gaussian convex spacelike hypersurfaces are not necessary hyperplanes without additional conditions. We show that a zero Gaussian curvature convex hypersurface must be a hyperplane if the mean curvature goes to zero at infinity. In the Minkowski context, we prove similar results for hypersurface without timelike points.
Cite
@article{arxiv.2601.08124,
title = {Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature},
author = {Slawomir Dinew and Mengru Guo and Heming Jiao},
journal= {arXiv preprint arXiv:2601.08124},
year = {2026}
}