Fast computation of analytic capacity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929380543954944 |
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| author | Nasser, Mohamed M S Green, Christopher C. Vuorinen, Matti |
| author_facet | Nasser, Mohamed M S Green, Christopher C. Vuorinen, Matti |
| contents | A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szegö kernel and then the value of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01808 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast computation of analytic capacity Nasser, Mohamed M S Green, Christopher C. Vuorinen, Matti Complex Variables 65E05, 30C40, 30C85, 65R20 A boundary integral equation method is presented for fast computation of the analytic capacities of compact sets in the complex plane. The method is based on using the Kerzman--Stein integral equation to compute the Szegö kernel and then the value of the Ahlfors map at the point at infinity. The proposed method can be used for domains with smooth and piecewise smooth boundaries. When combined with conformal mappings, the method can be used for compact slit sets. Several numerical examples are presented to demonstrate the efficiency of the proposed method. We recover some known exact results and corroborate the conjectural subadditivity property of analytic capacity. |
| title | Fast computation of analytic capacity |
| topic | Complex Variables 65E05, 30C40, 30C85, 65R20 |
| url | https://arxiv.org/abs/2307.01808 |