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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.05328 |
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| _version_ | 1866912945346183168 |
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| author | Dong, Xinlong G, Arshiya Farhath. Mitra, Sudeb |
| author_facet | Dong, Xinlong G, Arshiya Farhath. Mitra, Sudeb |
| contents | The Teichmüller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. Its complex structure follows from Lieb isomorphism. In this paper, we show the conformal naturality of Lieb isomorphism. We then study Douady-Earle section for these Teichmüller spaces. In particular, we study the real-analyticity of Douady-Earle section for classical Teichmüller spaces. We give two explicit examples of maximal holomorphic motions over simply connected complex Banach manifolds. As an application of the real-analyticity of the Douady-Earle section for the classical Teichmüller spaces of Riemann surfaces, we prove a new result showing that a family of Jordan curves varies real-analytically over a simply connected complex Banach manifold and as quasiconformal images of the one at the basepoint, provided that a finite number of marked points on the Jordan curves vary holomorphically over the same parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Teichmüller space of a closed set in the Riemann sphere Dong, Xinlong G, Arshiya Farhath. Mitra, Sudeb Complex Variables The Teichmüller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. Its complex structure follows from Lieb isomorphism. In this paper, we show the conformal naturality of Lieb isomorphism. We then study Douady-Earle section for these Teichmüller spaces. In particular, we study the real-analyticity of Douady-Earle section for classical Teichmüller spaces. We give two explicit examples of maximal holomorphic motions over simply connected complex Banach manifolds. As an application of the real-analyticity of the Douady-Earle section for the classical Teichmüller spaces of Riemann surfaces, we prove a new result showing that a family of Jordan curves varies real-analytically over a simply connected complex Banach manifold and as quasiconformal images of the one at the basepoint, provided that a finite number of marked points on the Jordan curves vary holomorphically over the same parameter space. |
| title | Teichmüller space of a closed set in the Riemann sphere |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.05328 |