Quadratic differentials, measured foliations and metric graphs on punctured surfaces
| Autor: | Dias, Kealey, Gupta, Subhojoy, Trnkova, Maria |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole-singularities. In a neighborhood of a pole such a foliation comprises foliated strips and half-planes, and its leaf-space determines a metric graph. We introduce the notion of an asymptotic direction at each pole, and show that for a punctured surface equipped with a choice of such asymptotic data, any compatible pair of measured foliations uniquely determines a complex structure and a meromorphic quadratic differential realizing that pair. This proves the analogue of a theorem of Gardiner-Masur, for meromorphic quadratic differentials. We also prove an analogue of the Hubbard-Masur theorem, namely, for a fixed punctured Riemann surface there exists a meromorphic quadratic differential with any prescribed horizontal foliation, and such a differential is unique provided we prescribe the singular-flat geometry at the poles. Comment: 32 pages, 9 figures |
| Databáze: | arXiv |
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