Abstract
We derive a Schwarz-Christoffel formula for the conformal mapping of an arbitrary n-connected domain D bounded by mutually disjoint circles ¦z − a k¦ = rk, k = 1,2,…,n, onto the exterior of mutually disjoint polygons. The derivation is based on the exact solution to a Riemann-Hilbert problem for D without any geometric restriction imposed upon the location of the non-overlapping disks ¦z − ak¦ ≤ rk.
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Mityushev, V. Schwarz-Christoffel Formula for Multiply Connected Domains. Comput. Methods Funct. Theory 12, 449–463 (2012). https://doi.org/10.1007/BF03321837
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DOI: https://doi.org/10.1007/BF03321837
En]Keywords
- Schwarz-Christoffel formula
- Riemann-Hilbert problem
- conformal mapping functional equation
- Poincaré series