Covering Properties of Meromorphic Functions, Negative Curvature and Spherical Geometry
Covering Properties of Meromorphic Functions, Negative Curvature and Spherical Geometry
Every non-constant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan √ 8 ≈ 70 • 32 .If in addition all critical points of the function are multiple, then a similar statement holds with π/2.These constants are best possible.The proof is based on the …