Simultaneous uniformization theorem: Difference between revisions

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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 surfacessurface]]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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==References==

*{{Citation | last1=Bers | first1=Lipman |authorlink=Lipman Bers| title=Simultaneous uniformization | doi=10.1090/S0002-9904-1960-10413-2 | idmr={{MR|0111834}} | year=1960 | journal=[[Bulletin of the American Mathematical Society]] | issn=0002-9904 | volume=66 | issue=2 | pages=94–97| doi-access=free }}

[[Category:Kleinian groups]]

[[Category:Riemann surfaces]]

{{Riemannian-geometry-stub}}