Conformal mapping of long quadrilaterals and thick doubly connected domains

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Abstract

In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of the rectangle to the four corners of the quadrilateral. Our main theorem tackles a conformal mapping problem for doubly connected domains, and we derive from this our results for quadrilaterals. As a corollary, we extend the "domain decomposition" mapping technique of Papamichael and Stylianopoulos. Similar results hold for the inverse maps, from quadrilaterals to rectangles.

Original languageEnglish (US)
Pages (from-to)523-554
Number of pages32
JournalConstructive Approximation
Volume10
Issue number4
DOIs
StatePublished - Dec 1994
Externally publishedYes

Keywords

  • AMS classification: Primary 30C35, Secondary 65E05, 30E10
  • Approximation
  • Conformal mapping
  • Quadrilaterals

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

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