https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Uniformization_theorem 2026-06-18T07:47:47Z Revision history for this page on the wiki MediaWiki 1.41.2 https://companal.subwiki.org/w/index.php?title=Uniformization_theorem&diff=613&oldid=prev 2008-09-12T20:44:17Z

<p>New page: ==Statement== There are two components to the statement: * Any simply connected <a href="/w/index.php?title=Fact_about::Riemann_surface&amp;action=edit&amp;redlink=1" class="new" title="Fact about::Riemann surface (page does not exist)">fact about::Riemann surface</a> is conformally equivalent to one of these three: the [[fact about::open uni...</p> <p><b>New page</b></p><div>==Statement==<br /> <br /> There are two components to the statement:<br /> * Any simply connected [[fact about::Riemann surface]] is conformally equivalent to one of these three: the [[fact about::open unit disk]], the [[fact about::complex plane]], the [[fact about::Riemann sphere]].<br /> * Any Riemann surface can be expressed as the quotient of its universal cover (which is one of these) by the action of the fundamental group (the quotient is in the sense of Riemann surfaces).<br /> <br /> ==Related facts==<br /> <br /> ===Particular cases/applications===<br /> <br /> * [[Genus zero Riemann surface is conformally equivalent to Riemann sphere]]: States that any compact, simply connected Riemann surface is conformally equivalent to the Riemann sphere.<br /> * [[Riemann mapping theorem]]</div>

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