On the asymptotic behavior of condenser capacity under blaschke products and universal covering maps

Dimitrios Betsakos, Georgios Kelgiannis, Maria Kourou, And Stamatis Pouliasis

Research output: Contribution to journalArticlepeer-review

Abstract

We prove an estimate for the capacity of the condenser (D,Kr), r ∈ (0, 1), where D is the open unit disc and {Kr} is a compact exhaustion of the inverse image of a compact set under a Blaschke product B, involving weighted logarithmic integral means of the Frostman shifts of B. Also, we describe the asymptotic behavior of the capacity of condensers (D,Er), where Er is a connected component of the inverse image of a closed disc with radius r under universal covering maps as r → 0.

Original languageEnglish
Pages (from-to)2963-2973
Number of pages11
JournalProceedings of the American Mathematical Society
Volume147
Issue number7
DOIs
StatePublished - 2019

Keywords

  • Blaschke products
  • Condenser capacity
  • Lindelöf principle
  • Universal covering maps

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