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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.

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

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

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

• 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.

• 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.

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