Conformal Invariants in Simply Connected Domains

Matti Vuorinen; Mohamed M S Nasser

Conformal Invariants in Simply Connected Domains

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arxiv 2001.10182 v1 pith:HX247Z2L submitted 2020-01-28 math.CV

Mohamed M S Nasser , Matti Vuorinen This is my paper · ORCID

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keywords severalconformalconnecteddomainsinvariantsmethodmodulusnumerical

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We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we use is based on the boundary integral equation with the generalized Neumann kernel. Several numerical examples are presented. We validate the performance and accuracy of our method by considering several model problems with known analytic solutions.

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Computation of conformal invariants
math.CV 2019-08 conditional novelty 6.0 of 10

A boundary integral equation method computes conformal capacity, hyperbolic capacity, and elliptic capacity for a wide class of planar doubly connected domains, with relative errors near 1e-14 on smooth test cases.

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