Modern proofs of it depend on the Stieltjes-Osgood theorem, and on an argument developed by Koebe whose name, in English, roughly translates as "cozying-up procedure.
Modern proofs of it depend on the Stieltjes-Osgood theorem, and on an argument developed by Koebe whose name, in English, roughly translates as "cozying-up procedure." It is unique in part because its analog for multiply connected domains is not true, and it is amazingly powerful, as it proves, for example, that any two simply connected domains in the plane are homeomorphic. For ten points, what is this, the ultimate theorem of undergraduate courses in complex analysis, named for a German mathematician?
Modern proofs of it depend on the Stieltjes-Osgood theorem, and on an argument developed by Koebe whose name, in English, roughly translates as "cozying-up procedure.
Riemann mapping theorem