Two characters on one punctured Riemann surface
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915828412186624 |
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| author | Kumar, Pradip |
| author_facet | Kumar, Pradip |
| contents | We develop an abstract framework for coupled period--realization of meromorphic $1$--forms on punctured Riemann surfaces. A configuration datum $C$ gives the combinatorics and determines a restricted character domain $Δ_C\subset\mathrm{Hom}(Γ_{g,n},{\mathbb C})^2$ with a scale--fixed slice $Δ_C^{\mathrm{sc}}$. Assuming Teichmüller--regularity, degeneration detection, and pushability, we prove that there is point in $Δ_C^{\mathrm{sc}}$ which corresponds to a surface carrying two meromorphic differentials realizing any prescribed restricted pair. This abstracts the Weber--Wolf extremal--length minimization method while constructing minimal surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two characters on one punctured Riemann surface Kumar, Pradip Geometric Topology Complex Variables Differential Geometry 57M50, 30F30, 32G15, 30F60 We develop an abstract framework for coupled period--realization of meromorphic $1$--forms on punctured Riemann surfaces. A configuration datum $C$ gives the combinatorics and determines a restricted character domain $Δ_C\subset\mathrm{Hom}(Γ_{g,n},{\mathbb C})^2$ with a scale--fixed slice $Δ_C^{\mathrm{sc}}$. Assuming Teichmüller--regularity, degeneration detection, and pushability, we prove that there is point in $Δ_C^{\mathrm{sc}}$ which corresponds to a surface carrying two meromorphic differentials realizing any prescribed restricted pair. This abstracts the Weber--Wolf extremal--length minimization method while constructing minimal surfaces. |
| title | Two characters on one punctured Riemann surface |
| topic | Geometric Topology Complex Variables Differential Geometry 57M50, 30F30, 32G15, 30F60 |
| url | https://arxiv.org/abs/2603.01905 |