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 language | English |
---|---|
Pages (from-to) | 113-133 |
Number of pages | 21 |
Journal | Annales Academiae Scientiarum Fennicae Mathematica |
Volume | 30 |
Issue number | 1 |
State | Published - 2005 |