Conformal mappings onto domains with arbitrarily specified boundary shapes

@article{Harrington1982ConformalMO,
  title={Conformal mappings onto domains with arbitrarily specified boundary shapes},
  author={A. N. Harrington},
  journal={Journal d’Analyse Math{\'e}matique},
  year={1982},
  volume={41},
  pages={39-53}
}
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Commentary by Dieter Gaier
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References

SHOWING 1-9 OF 9 REFERENCES
Finding zeroes of maps: homotopy methods that are constructive with probability one
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
Some problems related to iterative methods in conformal mapping
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.