Linked from

The 17 pages that link to Riemann mapping theorem, each with the reason it gives.

• Bernhard RiemannBroader topic: It exemplifies the reach of Riemann’s theory of conformal maps.

• Identity theoremRelated: The identity theorem supports uniqueness when comparing conformal maps with matching values.

• Conformal mapRelated: It guarantees a disk model for a broad class of planar domains.

• Möbius transformationRelated: Möbius maps provide explicit conformal equivalences for many basic domains.

• Cauchy–Riemann equationsRelated: It exemplifies the global geometric consequences of holomorphicity characterized locally by these equations.

• Schwarz lemmaRelated: Its normalized maps use the lemma to establish uniqueness.

• Uniformization theoremCompared with: It classifies planar domains, while uniformization classifies arbitrary simply connected Riemann surfaces.

• Circle packingRelated: Circle-packing approximations give discrete routes to conformal maps.

• Riemann sphereRelated: The sphere provides the global setting for understanding the theorem’s exceptional whole-plane case.

• Schwarz–Christoffel mappingNarrower topic: It guarantees a conformal map exists, while this method constructs one for polygons.

• Hurwitz's theoremRelated: Hurwitz's theorem helps establish that limits of injective holomorphic maps remain injective or degenerate.

• Constantin CarathéodoryRelated: Carathéodory's boundary results refine what the mapping theorem says about domain boundaries.

• Koebe quarter theoremRelated: The quarter theorem gives a size guarantee after a conformal map is normalized.

• Montel's theoremRelated: A normal-family compactness argument is central to a classical proof of the mapping theorem.

• Riemann–Hurwitz formulaCompared with: It is another foundational theorem named for Riemann, but concerns conformal equivalence rather than ramification.

• Schwarz reflection principleRelated: Reflection can extend conformal maps across sufficiently regular boundary arcs.

• Bloch's theorem (complex analysis)Related: Conformal maps express the image domains in the disk geometry used by Bloch-type estimates.