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In mathematics, the '''simultaneous uniformization theorem''', proved by {{harvtxt|Bers|1960}}, states that it is possible to simultaneously [[uniformization theorem|uniformize]] two different [[Riemann surface]]s of the same [[genus (mathematics)|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.
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[[Category:Kleinian groups]]
[[Category:Riemann surfaces]]
{{Riemannian-geometry-stub}}
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