Ahlfors five islands theorem
= Ahlfors five islands theorem
{c}
Every nonconstant <meromorphic function> on the complex plane has a <simple island> over at least one of any five <Jordan domains> on the <Riemann sphere> with disjoint closures. The <Ahlfors second fundamental theorem>, area comparison over target domains, and a <length-area exhaustion of the complex plane> prove this: without a simple island every counted island has degree at least two, forcing $3S\le(5/2)S+O(L)$.