Riemann mapping theorem


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Riemann mapping theorem

[′rē‚män ′map·iŋ ‚thir·əm]
(mathematics)
Any simply connected domain in the plane with boundary containing more than one point can be conformally mapped onto the interior of the unit disk.
References in periodicals archive ?
Among the topics are arithmetic and topology in the complex plane, holomorphic functions and differential forms, isolated singularities of holomorphic functions, harmonic functions, the Riemann mapping theorem and Dirichlet's problem, and the complex Fourier transform.
When talking about conformal mappings of a planar region onto another planar region a mathematician usually first thinks about complex analysis, the Riemann mapping theorem, and mapping with analytic functions.
INVERSE RIEMANN MAPPING THEOREM FOR RELATIVE CIRCLE DOMAINS.
In particular, the Riemann mapping theorem for relative circle domains stated in the introduction is proved.