Sharp estimates for hyperbolic metrics and covering theorems of Landau type

A. Baernstein, A. Eremenko, A. Fryntov, A. Solynin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

One of the main covering results asserts that if a holomorphic function f in the unit disk satisfies |f′(0)| ≥ A|f(0)| with A > 4, then f covers an annulus of the form r < |w| < Kr for some r > 0, where K is a certain function of A. Extremals are furnished by universal covering maps onto complements of certin discrete sets. The covering theorems are proved by solving minimum problems for hyperbolic metrics.

Original languageEnglish
Pages (from-to)113-133
Number of pages21
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume30
Issue number1
StatePublished - 2005

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