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Preprints, Working Papers, ... Year : 2016

Rational maps as Schwarzian primitives


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.
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Dates and versions

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



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