Resumen de Covering properties of meromorphic functions, negative curvature and spherical geometry

Alexandre Eremenko, Mario Bonk

• Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan¡î8 . 70.32¡Ç . If in addition all critical points of the function are multiple, then a similar statement holds with /2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.