Quasiconformal maps and substantial boundary points

J. M. Anderson, A. Hinkkanen

Research output: Contribution to journalArticlepeer-review

Abstract

Let D be a bounded domain in ℂ with ζ0 ε ∂D. We say that ζ0 is a substantial boundary point of D for the affine stretch x+iy → Kx+iy, where K > 1, if for every neighbourhood U of ζ0 and for every component V of U ∩ D with ζ0 ε ∂V, the maximal dilatation of f is at least K for every quasiconformal map f of V such that f(x + iy) = Kx + iy for all x + iy ε ∂V ∩ ∂D. We give here a criterion for a point ζ0 to be a substantial boundary point for the affine stretch in D - Theorem 1.1 below. This will depend on the "narrowness" of D near ζ0 though the particular way that D is narrow may vary, as we shall show.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalPure and Applied Mathematics Quarterly
Volume7
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Affine stretch
  • Quasiconformal mappings
  • Substantial boundary points

ASJC Scopus subject areas

  • Mathematics(all)

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