Uniformization of simply connected finite type log-Riemann surfaces
Complex Variables
2010-11-04 v1
Abstract
We consider simply connected log-Riemann surfaces with a finite number of ramification points. We prove that these surfaces are biholomorphic to C with uniformizations given by entire functions of the form F (z) = \int Q(z) e^{P(z)} dz where P, Q are polynomials of degrees equal to the number of infinite and finite order ramification points respectively. Conversely any such entire function defines a simply connected log-Riemann surface with finitely many ramification points.
Keywords
Cite
@article{arxiv.1011.0812,
title = {Uniformization of simply connected finite type log-Riemann surfaces},
author = {Kingshook Biswas and Ricardo Perez-Marco},
journal= {arXiv preprint arXiv:1011.0812},
year = {2010}
}
Comments
13 pages