A survey on Bernstein-type theorems for entire graphical surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916884460339200 |
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| author | Kawakami, Yu |
| author_facet | Kawakami, Yu |
| contents | We survey Bernstein-type theorems for graphical surfaces in the Euclidean space and the Lorentz-Minkowski space. More specifically, we explain several proofs of the Bernstein theorem for minimal graphs in the Euclidean 3-space. Furthermore, we show the Heinz-type mean curvature estimates for graphs in the Euclidean 3-space and space-like graphs in the Lorentz-Minkowski 3-space. As an application of these estimates, we give Bernstein-type theorems for constant mean curvature graphs in the Euclidean 3-space and constant mean curvature space-like graphs in the Lorentz-Minkowski 3-space, respectively. We also study Bernstein-type results for minimal graphs in the Euclidean 4-space and the Calabi-Bernstein theorem in the Lorentz-Minkowski 3-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A survey on Bernstein-type theorems for entire graphical surfaces Kawakami, Yu Differential Geometry Analysis of PDEs Complex Variables Primary 53A10, Secondary 35J93, 53C24 We survey Bernstein-type theorems for graphical surfaces in the Euclidean space and the Lorentz-Minkowski space. More specifically, we explain several proofs of the Bernstein theorem for minimal graphs in the Euclidean 3-space. Furthermore, we show the Heinz-type mean curvature estimates for graphs in the Euclidean 3-space and space-like graphs in the Lorentz-Minkowski 3-space. As an application of these estimates, we give Bernstein-type theorems for constant mean curvature graphs in the Euclidean 3-space and constant mean curvature space-like graphs in the Lorentz-Minkowski 3-space, respectively. We also study Bernstein-type results for minimal graphs in the Euclidean 4-space and the Calabi-Bernstein theorem in the Lorentz-Minkowski 3-space. |
| title | A survey on Bernstein-type theorems for entire graphical surfaces |
| topic | Differential Geometry Analysis of PDEs Complex Variables Primary 53A10, Secondary 35J93, 53C24 |
| url | https://arxiv.org/abs/2403.14199 |