A2 Refereed review article in a scientific journal
On Computation of Capacities and Conformal Invariants
Authors: Nasser, Mohamed M. S.; Vuorinen, Matti
Publisher: Springer Science and Business Media LLC
Publication year: 2026
Journal: Journal of Mathematical Sciences
ISSN: 1072-3374
eISSN: 1573-8795
DOI: https://doi.org/10.1007/s10958-025-08141-0
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1007/s10958-025-08141-0
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/523213474
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
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.
Downloadable publication This is an electronic reprint of the original article. |  |
Funding information in the publication:
Open Access funding provided by University of Turku (including Turku University Central Hospital).
