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Showing 1 to 3 of 3 for “"Riemann Map"”.
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The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps
The well-known Riemann Mapping Theorem states the existence of a conformal map of a simply connected proper domain of the complex plane onto the upper half plane. One of the main topics in geometric function theory is to investigate the behaviour of the mapping functions at the boundary of such …
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High-order numerical methods for layer potential evaluation
… potentials to the problem of numerical conformal mapping. It is shown how there is a strong connection between the double-layer potential and the Faber/Faber-Laurent polynomials, which are polynomials closely related to the series expansion of the Riemann map. From this, a scheme for computing the …
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Discrete Riemann Maps and the Parabolicity of Tilings
The classical Riemann Mapping Theorem has many discrete analogues. One of these, the Finite Riemann Mapping Theorem of Cannon, Floyd, Parry, and others, describes finite tilings of quadrilaterals and annuli. It relates to several combinatorial moduli, similar in nature to the classical modulus. The …