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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.20486 |
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| _version_ | 1866915467853037568 |
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| author | Kuo, Ting-Jung Liang, Xuanpu Wu, Ping-Hsiang |
| author_facet | Kuo, Ting-Jung Liang, Xuanpu Wu, Ping-Hsiang |
| contents | Motivated by the finite-gap structure of the classical Lamé equation (1.2) and its central role in mathematical physics, generalized Lamé-type equations (1.12) are investigated. For the fundamental case $n=1$, a monodromy equivalence between the classical Lamé equation (1.18) and the generalized Lamé-type equation (1.19) is established. Two main applications are obtained: (i) the finite-gap structure of \ (1.19) is derived, together with a complete classification of the spectral curves $σ_{1}$ and $σ_{2}$ for $τ\in i\mathbb{R}_{>0}$; and (ii) the monodromy equivalence is applied to the construction of cone spherical metrics with three large conical singularities, each with cone angle exceeding $2π$. A family of such metrics is shown to exhibits a blow-up configuration, which is described explicitly in terms of the monodromy data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monodromy Equivalence for Lamé-type Equations I: Finite-gap Structures and Cone Spherical Metrics Kuo, Ting-Jung Liang, Xuanpu Wu, Ping-Hsiang Classical Analysis and ODEs Analysis of PDEs Differential Geometry 58J10, 53A10 Motivated by the finite-gap structure of the classical Lamé equation (1.2) and its central role in mathematical physics, generalized Lamé-type equations (1.12) are investigated. For the fundamental case $n=1$, a monodromy equivalence between the classical Lamé equation (1.18) and the generalized Lamé-type equation (1.19) is established. Two main applications are obtained: (i) the finite-gap structure of \ (1.19) is derived, together with a complete classification of the spectral curves $σ_{1}$ and $σ_{2}$ for $τ\in i\mathbb{R}_{>0}$; and (ii) the monodromy equivalence is applied to the construction of cone spherical metrics with three large conical singularities, each with cone angle exceeding $2π$. A family of such metrics is shown to exhibits a blow-up configuration, which is described explicitly in terms of the monodromy data. |
| title | Monodromy Equivalence for Lamé-type Equations I: Finite-gap Structures and Cone Spherical Metrics |
| topic | Classical Analysis and ODEs Analysis of PDEs Differential Geometry 58J10, 53A10 |
| url | https://arxiv.org/abs/2508.20486 |