Conformal mappings onto domains with arbitrarily specified boundary shapes

  title={Conformal mappings onto domains with arbitrarily specified boundary shapes},
  author={A. N. Harrington},
  journal={Journal d’Analyse Math{\'e}matique},
Uniformization by rectangular domains: A path from slits to squares
Abstract Let Σ ( Ω ) be the class of functions f ( z ) = z + a 1 z + ⋯ univalent on a finitely connected domain Ω, ∞ ∈ Ω ⊂ C ‾ . By a classical result due to H. Grotzsch, the function f 0 maximizingExpand
Domain-filling circle packings
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This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting theExpand
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A relative Schottky set in a planar domain D is a subset of D obtained by removing from D open geometric discs whose closures are in D and are pairwise disjoint. In this paper we study quasisymmetricExpand
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Commentary by Dieter Gaier


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We illustrate that most existence theorems using degree theory are in principle relatively constructive. The first one presented here is the Brouwer Fixed Point Theorem. Our method is "constructiveExpand
A homotopy method for locating all zeros of a system of polynomials
In [2] the authors gave a constructive proof of the Brouwer fixed point theorem by means of a homotopy (continuation) method. The basic idea used in the proof is the concept of transversality; otherExpand
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On the conformal mapping of multiply connected regions
It is the object of this paper to set forth a proof of Theorem 1 below, to the effect that an arbitrary plane region D bounded by a finite number of mutually disjoint Jordan curves can be mapped oneExpand
The Location of Critical Points of Analytic and Harmonic Functions
The best ebooks about The Location Of Critical Points Of Analytic And Harmonic Functions that you can get for free here by download this The Location Of Critical Points Of Analytic And HarmonicExpand
Uniqueness Theorems for Conformal Mapping of Multiply Connected Domains.
  • M. Shiffman
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1941
A General Theorem on Conformal Mapping of Multiply Connected Domains.