Bernstein-type Theorems for constant mean curvature surfaces in the three-dimensional light cone
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915872127320064 |
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| author | Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog |
| author_facet | Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog |
| contents | We establish Bernstein-type theorems for entire constant mean curvature graphs in the three-dimensional light cone $\mathbb{Q}^3_+$ over the horosphere under the assumption that the Gaussian curvature $K$ is bounded below, by showing that such graphs are horospheres or spheres of $\mathbb{Q}^3_+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bernstein-type Theorems for constant mean curvature surfaces in the three-dimensional light cone Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog Differential Geometry (2020) Primary 53A10, Secondary 53B30, 35B08 We establish Bernstein-type theorems for entire constant mean curvature graphs in the three-dimensional light cone $\mathbb{Q}^3_+$ over the horosphere under the assumption that the Gaussian curvature $K$ is bounded below, by showing that such graphs are horospheres or spheres of $\mathbb{Q}^3_+$. |
| title | Bernstein-type Theorems for constant mean curvature surfaces in the three-dimensional light cone |
| topic | Differential Geometry (2020) Primary 53A10, Secondary 53B30, 35B08 |
| url | https://arxiv.org/abs/2603.17727 |