Rational maps as Schwarzian primitives
Complex Variables
2016-08-24 v2
Abstract
We study necessary and sufficient conditions for a meromorphic quadratic differential with prescribed poles to be the Schwarzian derivative of a rational map. We give geometric interpretations of these conditions. We also study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case, the analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.
Keywords
Cite
@article{arxiv.1511.04246,
title = {Rational maps as Schwarzian primitives},
author = {Guizhen Cui and Yan Gao and Lei Tan and Rugh Hans Henrik},
journal= {arXiv preprint arXiv:1511.04246},
year = {2016}
}