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On computation of capacities and conformal invariants
Nasser, Mohamed M. S. Vuorinen, Matti
Nasser, Mohamed M. S.
Vuorinen, Matti
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Issue Date
2026-03-12
Type
Review
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Keywords
Boundary integral equation method,Capacity computation,Condenser capacity,Generalized Neumann kernel,Multiply connected domains
Subjects (LCSH)
Citation
Nasser, M., Vuorinen, M. ON COMPUTATION OF CAPACITIES AND CONFORMAL INVARIANTS. J Math Sci (2026). https://doi.org/10.1007/s10958-025-08141-0
Abstract
We give a survey of the 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 the mixed Dirichlet-Neumann boundary value problem for the Laplace equation has a key role. At the end of the paper, we give a topic-wise structured list of our extensive bibliography on constructive complex analysis and potential theory. © The Author(s) 2026.
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This is an open access article under the CC BY license.
Publisher
Springer
Journal
Journal of Mathematical Sciences (United States)
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PubMed ID
ISSN
10723374