Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918039179493376 |
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| author | Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog |
| author_facet | Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog |
| contents | There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in $\mathbb{I}^3$, which implies a Bernstein-type theorem for CMC $H$ graphs in $\mathbb{I}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space Akamine, Shintaro Lee, Wonjoo Yang, Seong-Deog Differential Geometry Primary 53A10, Secondary 53B30, 35B08 There are many non-trivial entire spacelike graphs with constant mean curvature $H$ (CMC $H$, for short) in the isotropic 3-space $\mathbb{I}^3$. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in $\mathbb{I}^3$, which implies a Bernstein-type theorem for CMC $H$ graphs in $\mathbb{I}^3$. |
| title | Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space |
| topic | Differential Geometry Primary 53A10, Secondary 53B30, 35B08 |
| url | https://arxiv.org/abs/2505.24109 |