Covering properties of meromorphic functions, negative curvature and spherical geometry
Complex Variables
2016-09-07 v1
Abstract
Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan(sqrt 8) ~ 70^\circ 32'. If in addition all critical points of the function are multiple, then a similar statement holds with pi/2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.
Keywords
Cite
@article{arxiv.math/0009251,
title = {Covering properties of meromorphic functions, negative curvature and spherical geometry},
author = {Mario Bonk and Alexandre Eremenko},
journal= {arXiv preprint arXiv:math/0009251},
year = {2016}
}
Comments
42 pages, published version