Toda lattice and Riemann type minimal surfaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909297463525376 |
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| author | Gui, Changfeng Liu, Yong Wang, Jun Yang, Wen |
| author_facet | Gui, Changfeng Liu, Yong Wang, Jun Yang, Wen |
| contents | Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing configuration using techniques of integrable systems. This allows us to construct new singly periodic minimal surfaces. The genus of these minimal surfaces equals $j(j+1)/2-1$. They are natural generalization of the Riemann minimal surfaces, which have genus zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toda lattice and Riemann type minimal surfaces Gui, Changfeng Liu, Yong Wang, Jun Yang, Wen Exactly Solvable and Integrable Systems Analysis of PDEs Differential Geometry Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing configuration using techniques of integrable systems. This allows us to construct new singly periodic minimal surfaces. The genus of these minimal surfaces equals $j(j+1)/2-1$. They are natural generalization of the Riemann minimal surfaces, which have genus zero. |
| title | Toda lattice and Riemann type minimal surfaces |
| topic | Exactly Solvable and Integrable Systems Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2408.14924 |