Minimal Lagrangian surfaces in $\mathbb{C}P^2$ via the loop group method Part II: The general case
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910436197138432 |
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| author | Dorfmeister, Josef F. Ma, Hui |
| author_facet | Dorfmeister, Josef F. Ma, Hui |
| contents | We extend the techniques introduced in \cite{DoMaB1} for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into $\mathbb{C}P^2$ via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in $\mathbb{C}P^2$ and construct a class of minimal Lagrangian cylinders. Furthermore, we show that these minimal Lagrangian cylinders approximate Delaunay cylinders with respect to some weighted Wiener norm of the twisted loop group $ΛSU(3)_σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal Lagrangian surfaces in $\mathbb{C}P^2$ via the loop group method Part II: The general case Dorfmeister, Josef F. Ma, Hui Differential Geometry 53C42, 53D12 We extend the techniques introduced in \cite{DoMaB1} for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into $\mathbb{C}P^2$ via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in $\mathbb{C}P^2$ and construct a class of minimal Lagrangian cylinders. Furthermore, we show that these minimal Lagrangian cylinders approximate Delaunay cylinders with respect to some weighted Wiener norm of the twisted loop group $ΛSU(3)_σ$. |
| title | Minimal Lagrangian surfaces in $\mathbb{C}P^2$ via the loop group method Part II: The general case |
| topic | Differential Geometry 53C42, 53D12 |
| url | https://arxiv.org/abs/2405.03246 |