On the Hyperbolic Metric of Certain Domains

Aimo Hinkkanen, Matti Vuorinen

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that if E is a compact subset of the unit disk D in the complex plane, if E contains a sequence of distinct points an≠ 0 for n≥ 1 such that lim nan= 0 and for all n we have | an+1| ≥ | an| / 2 , and if G= D\ E is connected and 0 ∈ ∂G , then there is a constant c> 0 such that for all z∈ G we have λG(z) ≥ c/ | z| where λG(z) is the density of the hyperbolic metric in G.

Original languageEnglish (US)
JournalComputational Methods and Function Theory
DOIs
StateAccepted/In press - 2024

Keywords

  • Analytic function
  • Conformal invariant
  • Hyperbolic metric

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

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