A model of the Teichmüller space of genus-zero bordered surfaces by period maps. (English) Zbl 1426.30031
The period mappings of compact surfaces are known to be one of the useful ways of associating complex structures on Teichmüller space. Generalizing this well-known fact, in this paper, the authors give a new construction enabling the idea to infinite dimension by showing that the generalized period mapping defines a new complex structure on the Teichmüller space of genus zero having \(n\) borders.
The authors make a guess about the extendibility of this case to non-zero-genus surfaces with boundary and also they state that there are many properties of this model which can be obtained by classical methods
The authors make a guess about the extendibility of this case to non-zero-genus surfaces with boundary and also they state that there are many properties of this model which can be obtained by classical methods
Reviewer: Ismail Naci Cangül (Bursa)
MSC:
| 30F60 | Teichmüller theory for Riemann surfaces |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
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