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arXiv · 1511.04246

Rational maps as Schwarzian primitives

Guizhen Cui·Yan Gao·Lei Tan·Rugh Hans Henrik
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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.

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Guizhen Cui, Yan Gao, Lei Tan, Rugh Hans Henrik. 2016-01-25. Rational maps as Schwarzian primitives. https://doi.org/10.1007/s11425-016-5140-7

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