Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917198738489344 |
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| author | Dinew, Slawomir Guo, Mengru Jiao, Heming |
| author_facet | Dinew, Slawomir Guo, Mengru Jiao, Heming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08124 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature Dinew, Slawomir Guo, Mengru Jiao, Heming Differential Geometry Analysis of PDEs 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. |
| title | Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2601.08124 |