Kleinian groups | Riemann surfaces

Simultaneous uniformization theorem

In mathematics, the simultaneous uniformization theorem, proved by , states that it is possible to simultaneously uniformize two different Riemann surfaces of the same genus using a quasi-Fuchsian group of the first kind. The quasi-Fuchsian group is essentially uniquely determined by the two Riemann surfaces, so the space of marked quasi-Fuchsian group of the first kind of some fixed genus g can be identified with the product of two copies of Teichmüller space of the same genus. (Wikipedia).

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Related pages

Riemann surface | Quasi-Fuchsian group | Teichmüller space | Uniformization theorem | Genus (mathematics)