Genus one $H$-surfaces with $k$-ends in $\mathbb{H}^2\times\mathbb{R}$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929565518004224 |
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| author | Castro-Infantes, Jesús Santiago, José S. |
| author_facet | Castro-Infantes, Jesús Santiago, José S. |
| contents | We construct two different families of properly Alexandrov-immersed surfaces in $\mathbb{H}^2\times \mathbb{R}$ with constant mean curvature $0<H\leq \frac 1 2$, genus one and $k\geq2$ ends ($k=2$ only for one of these families). These ends are asymptotic to vertical $H$-cylinders for $0<H<\frac 1 2$. This shows that there is not a Schoen-type theorem for immersed surfaces with positive constant mean curvature in $\mathbb{H}^2\times\mathbb{R}$. These surfaces are obtained by means of a conjugate construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17433 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Genus one $H$-surfaces with $k$-ends in $\mathbb{H}^2\times\mathbb{R}$ Castro-Infantes, Jesús Santiago, José S. Differential Geometry We construct two different families of properly Alexandrov-immersed surfaces in $\mathbb{H}^2\times \mathbb{R}$ with constant mean curvature $0<H\leq \frac 1 2$, genus one and $k\geq2$ ends ($k=2$ only for one of these families). These ends are asymptotic to vertical $H$-cylinders for $0<H<\frac 1 2$. This shows that there is not a Schoen-type theorem for immersed surfaces with positive constant mean curvature in $\mathbb{H}^2\times\mathbb{R}$. These surfaces are obtained by means of a conjugate construction. |
| title | Genus one $H$-surfaces with $k$-ends in $\mathbb{H}^2\times\mathbb{R}$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2306.17433 |