Constructing entire minimal graphs by evolving planes
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917142157328384 |
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| author | Tsai, Chung-Jun Tsui, Mao-Pei Wan, Jingbo Wang, Mu-Tao |
| author_facet | Tsai, Chung-Jun Tsui, Mao-Pei Wan, Jingbo Wang, Mu-Tao |
| contents | We introduce an evolving-plane ansatz for the explicit construction of entire minimal graphs of dimension $n$ ($n\geq 3$) and codimension $m$ ($m\geq 2$), for any odd integer $n$. Under this ansatz, the minimal surface system reduces to the geodesic equation on the Grassmannian in affine coordinates. Geometrically, this equation dictates how the slope of an $(n-1)$ plane evolves as it sweeps out a minimal graph. This framework yields a rich family of explicit entire minimal graphs of odd dimension $n$ and arbitrary codimension $m$. For each entire minimal graph, its conormal bundle gives rise to an entire special Lagrangian graph in $\mathbb{C}^{n+m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing entire minimal graphs by evolving planes Tsai, Chung-Jun Tsui, Mao-Pei Wan, Jingbo Wang, Mu-Tao Differential Geometry Analysis of PDEs 58E12, 58E15 (Primary), 35J47, 35J60(Secondary) We introduce an evolving-plane ansatz for the explicit construction of entire minimal graphs of dimension $n$ ($n\geq 3$) and codimension $m$ ($m\geq 2$), for any odd integer $n$. Under this ansatz, the minimal surface system reduces to the geodesic equation on the Grassmannian in affine coordinates. Geometrically, this equation dictates how the slope of an $(n-1)$ plane evolves as it sweeps out a minimal graph. This framework yields a rich family of explicit entire minimal graphs of odd dimension $n$ and arbitrary codimension $m$. For each entire minimal graph, its conormal bundle gives rise to an entire special Lagrangian graph in $\mathbb{C}^{n+m}$. |
| title | Constructing entire minimal graphs by evolving planes |
| topic | Differential Geometry Analysis of PDEs 58E12, 58E15 (Primary), 35J47, 35J60(Secondary) |
| url | https://arxiv.org/abs/2510.24978 |