Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains

@article{Vasconcelos2014GeneralizationOT,
  title={Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains},
  author={Giovani L. Vasconcelos},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2014},
  volume={470}
}
  • G. L. Vasconcelos
  • Published 3 March 2014
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
A generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function… 

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References

SHOWING 1-10 OF 13 REFERENCES

Schwarz–Christoffel mappings to unbounded multiply connected polygonal regions

  • D. Crowdy
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2007
Abstract A formula for the generalized Schwarz–Christoffel conformal mapping from a bounded multiply connected circular domain to an unbounded multiply connected polygonal domain is derived. The

Schwarz-Christoffel mapping of multiply connected domains

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivitym≥2 thereby extending the results of Christoffel (1867) and Schwarz (1869) form=1 and Komatu

The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains

  • D. Crowdy
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2005
A formula for the generalized Schwarz–Christoffel mapping from a bounded multiply connected circular domain to a bounded multiply connected polygonal domain is derived. The theory of classical

SLIT MAPS AND SCHWARZ-CHRISTOFFEL MAPS FOR MULTIPLY CONNECTED DOMAINS

We review recent derivations of formulas for conformal maps from finitely connected domains with circular holes to canonical radial or circular slit domains . The formulas are infinite products based

Multiple steadily translating bubbles in a Hele-Shaw channel

Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles.

Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions

1. The subject of investigation 2. The fundamental functions on a Riemann surface 3. The infinities of rational functions 4. Specification of a general form of Riemann's integrals 5. Certain forms of

Conformal Mappings between Canonical Multiply Connected Domains

Explicit analytical formulae for the conformal mappings from the canonical class of multiply connected circular domains to canonical classes of multiply connected slit domains are constructed. All

Explicit solution of a class of Riemann-Hilbert problems

Analytical solutions to a special class of Riemann-Hilbert boundary value problems on multiply connected domains are presented. The solutions are written, up to a finite number of accessory

Complex Variables: Introduction and Applications

Part I. 1. Complex numbers and elementary functions 2. Analytic functions and integration 3. Sequences, series and singularities of complex functions 4. Residue calculus and applications of contour

Schwarz-Christoffel Mapping

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