A Note on Helicoidal Singular Minimal Surfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908455502086144 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | Let $α\in\r$ and let $\vec{v}\in\r^3$ be a unit vector. A singular minimal surface $Σ$ in Euclidean space is a surface $Σ$ whose mean curvature $H$ satisfies $H=α\frac{\langle N,\vec{v}\rangle}{\langle p,\vec{v}\rangle}$, where $N$ is the unit normal vector of $Σ$. In this short note we study singular minimal surfaces which are invariant by a one-parameter group of helicoidal motions. We prove that if $Σ$ is a helicoidal singular minimal surface, then the axis of the helicoidal motion is orthogonal to $\vec{v}$, $α=-1$ and $Σ$ is a circular right cylinder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on Helicoidal Singular Minimal Surfaces López, Rafael Differential Geometry 53A10, 53C24, 53E10 Let $α\in\r$ and let $\vec{v}\in\r^3$ be a unit vector. A singular minimal surface $Σ$ in Euclidean space is a surface $Σ$ whose mean curvature $H$ satisfies $H=α\frac{\langle N,\vec{v}\rangle}{\langle p,\vec{v}\rangle}$, where $N$ is the unit normal vector of $Σ$. In this short note we study singular minimal surfaces which are invariant by a one-parameter group of helicoidal motions. We prove that if $Σ$ is a helicoidal singular minimal surface, then the axis of the helicoidal motion is orthogonal to $\vec{v}$, $α=-1$ and $Σ$ is a circular right cylinder. |
| title | A Note on Helicoidal Singular Minimal Surfaces |
| topic | Differential Geometry 53A10, 53C24, 53E10 |
| url | https://arxiv.org/abs/2507.13669 |