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Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.08124

Authors: Dinew, Slawomir, Guo, Mengru, Jiao, Heming

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Scholarship Council

Award: G133574114

OpenAlex ID: W7124143916

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