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.
|Number of pages||21|
|Journal||Annales Academiae Scientiarum Fennicae Mathematica|
|State||Published - 2005|