On computation of capacities and conformal invariants
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915625949986816 |
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| author | Nasser, Mohamed M S Vuorinen, Matti |
| author_facet | Nasser, Mohamed M S Vuorinen, Matti |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On computation of capacities and conformal invariants Nasser, Mohamed M S Vuorinen, Matti Complex Variables 65E05, 31A15, 30C85 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. |
| title | On computation of capacities and conformal invariants |
| topic | Complex Variables 65E05, 31A15, 30C85 |
| url | https://arxiv.org/abs/2507.11648 |