Rational maps as Schwarzian primitives - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

Rational maps as Schwarzian primitives

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.
Fichier principal
Vignette du fichier
SCM-2015-0520.pdf (500.41 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01228525 , version 1 (13-11-2015)
hal-01228525 , version 2 (24-01-2016)

Identifiers

Cite

Guizhen Cui, Yan Gao, Lei Tan, Rugh Hans Henrik. Rational maps as Schwarzian primitives. 2016. ⟨hal-01228525v2⟩
121 View
175 Download

Altmetric

Share

Gmail Facebook X LinkedIn More