Numerical conformal mapping
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909696803209216 |
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| author | Trefethen, Lloyd N. |
| author_facet | Trefethen, Lloyd N. |
| contents | Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $Ω$ in the complex plane ${\mathbb{C}}$ (assuming $Ω\ne {\mathbb{C}}$) can be mapped bijectively to the unit disk by an analytic function with nonvanishing derivative, as in Figure 1. If $Ω$ is doubly-connected, it can be mapped to a circular annulus $1<|z|<R$ for some $R$, called the conformal modulus, which is uniquely determined by $Ω$, as in Figure 2. If $Ω$ has connectivity higher than $2$, it can be mapped onto various canonical domains such as a disk with exclusions in the form of slits or smaller disks, as in Figure 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical conformal mapping Trefethen, Lloyd N. Complex Variables 65E10 Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $Ω$ in the complex plane ${\mathbb{C}}$ (assuming $Ω\ne {\mathbb{C}}$) can be mapped bijectively to the unit disk by an analytic function with nonvanishing derivative, as in Figure 1. If $Ω$ is doubly-connected, it can be mapped to a circular annulus $1<|z|<R$ for some $R$, called the conformal modulus, which is uniquely determined by $Ω$, as in Figure 2. If $Ω$ has connectivity higher than $2$, it can be mapped onto various canonical domains such as a disk with exclusions in the form of slits or smaller disks, as in Figure 3. |
| title | Numerical conformal mapping |
| topic | Complex Variables 65E10 |
| url | https://arxiv.org/abs/2507.14872 |