The Schottky-Klein prime function on the Schottky double of planar domains

DOI10.1007/BF03321778zbMath1217.30005OpenAlexW1978371271MaRDI QIDQ619443

Darren G. Crowdy

Publication date: 25 January 2011

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321778

zbMATH Keywords

conformal mappingsslit mappingsSchottky-Klein prime functionSchwarz-Christoffel

Mathematics Subject Classification ID

Conformal mappings of special domains (30C20) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (13)

Quantized point vortex equilibria in a one-way interaction model with a Liouville-type background vorticity on a curved torus ⋮ Poincaré $$\boldsymbol{\alpha }$$ -Series for Classical Schottky Groups ⋮ Analytical solutions for annular multipolar vortex equilibria on a sphere ⋮ Efficient calculation of Schwarz-Christoffel transformations for multiply connected domains using Laurent series ⋮ Shape calculus for vortex patch equilibria and its application to lattice configurations ⋮ The Schottky–Klein Prime Function ⋮ The \(N\)-vortex problem in a doubly periodic rectangular domain with constant background vorticity ⋮ On the uniqueness problem for quadrature domains ⋮ CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS ⋮ The squeezing function on doubly-connected domains via the Loewner differential equation ⋮ Conformal mappings to multiply connected polycircular arc domains ⋮ Calculation of resistances for multiply connected domains using Schwarz-Christoffel transformations ⋮ A PAIR OF PERFECTLY CONDUCTING DISKS IN AN EXTERNAL FIELD

Uses Software

• Schwarz-Christoffel
• SC Toolbox
• SKPrime

Cites Work

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• Schwarz-Christoffel mapping of bounded, multiply connected domains
• Computation of multiply connected Schwarz-Christoffel maps for exterior domains
• Theta functions on Riemann surfaces
• Quadrature identities and the Schottky double
• Prime form and Schottky model
• Computing the Schottky-Klein prime function on the Schottky double of planar domains
• Conformal mappings between canonical multiply connected domains
• Schwarz-Christoffel mapping of multiply connected domains
• Schwarz--Christoffel Mapping of the Annulus
• Schwarz–Christoffel mappings to unbounded multiply connected polygonal regions
• Schwarz-Christoffel Mapping
• Computing Riemann theta functions
• Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains
• The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains
• Theta functions, kernel functions, and Abelian integrals

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