Linked from

The 29 pages that link to Conformal map, each with the reason it gives.

• Holomorphic functionRelated: Holomorphic functions with nonzero derivative generate conformal maps.

• Complex analysisRelated: Holomorphic functions provide maps used to simplify planar geometry and boundary-value problems.

• Laplace's equationRelated: In two dimensions, conformal maps preserve harmonicity and help construct solutions.

• IsometryCompared with: Conformal maps preserve local angles, not necessarily distances or scale.

• Harmonic functionRelated: In two dimensions, conformal maps transport harmonic functions between domains.

• Riemann mapping theoremBroader topic: The theorem asserts the existence of a conformal map from each eligible domain to the disk.

• Riemann surfaceRelated: Conformal equivalence captures when two Riemann surfaces have the same complex geometry.

• Möbius transformationNarrower topic: Away from its pole, a Möbius transformation preserves angles and orientation.

• Cauchy–Riemann equationsRelated: Complex differentiability satisfying the equations gives local angle preservation when the derivative is nonzero.

• Schwarz lemmaNarrower topic: The lemma constrains normalized conformal maps between disk domains.

• Uniformization theoremNarrower topic: Conformal equivalence is the relation asserted between a simply connected surface and its model.

• Change of variablesRelated: Conformal maps are specialized variable changes that preserve local angles but may distort lengths.

• Complex differentiabilityRelated: A nonzero complex derivative acts as local scaling and rotation, producing angle preservation.

• Potential theoryRelated: In two dimensions, conformal maps transport harmonic functions and simplify boundary problems.

• Similarity transformationRelated: Conformal maps share angle preservation but can vary scale from point to point.

• Dirichlet problemRelated: In two dimensions, conformal maps transfer harmonic Dirichlet problems between suitable domains.

• Circle packingRelated: Conformal maps connect circle packings to the geometry of planar domains.

• Rhumb lineRelated: Angle preservation helps explain why Mercator charts retain a rhumb line's crossing angle.

• Riemann sphereRelated: Spherical coordinates let conformal maps include neighborhoods of infinity.

• Stereographic projectionNarrower topic: Stereographic projection is a concrete conformal map between the punctured sphere and the plane.

• Schwarz–Christoffel mappingNarrower topic: Schwarz–Christoffel mappings are a polygon-specific family of conformal maps.

• Montel's theoremRelated: Compactness of holomorphic families became a powerful method for proving mapping results.

• Circle packing theoremRelated: Circle packings approximate conformal maps as the mesh becomes finer.

• Schwarz reflection principleNarrower topic: Extending a conformal map can reveal its behavior beyond the original domain.

• Inversive geometryNarrower topic: Inversion is angle-preserving away from its center, linking the geometry to conformal mapping.

• Nikolay ZhukovskyNarrower topic: It provides the mathematical method behind the Joukowski airfoil construction.

• Brennan conjectureNarrower topic: The conjecture quantifies the derivative of maps in this class.

• De Branges's theoremNarrower topic: Univalent functions provide conformal maps, so coefficient bounds constrain their geometry.

• Methods in electromagnetismRelated: It can turn difficult two-dimensional electrostatic boundary shapes into solvable ones.