On computation of capacities and conformal invariants

Mohamed M S Nasser; Matti Vuorinen

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arXiv · 2507.11648

On computation of capacities and conformal invariants

Mohamed M S Nasser·Matti Vuorinen

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Abstract

We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary integral equation with the generalized Neumann kernel to the computation of several other conformal invariants: harmonic measure, modulus of a quadrilateral, reduced modulus, hyperbolic capacity, and elliptic capacity. Here the solution of mixed Dirichlet-Neumann boundary value problem for the Laplace equation has a key role. At the end of the paper we give a topicwise structured list to our extensive bibliography on constructive complex analysis and potential theory.

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Mohamed M S Nasser, Matti Vuorinen. 2025-07-15. On computation of capacities and conformal invariants. https://arxiv.org/abs/2507.11648

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