Piecewise geodesic Jordan curves I: weldings, explicit computations, and Schwarzian derivatives

Donald Marshall, Steffen Rohde, Yilin Wang

We consider Jordan curves of the form $\gamma ={\cup }_{j=1}^n{\gamma }_j$ on the Riemann sphere for which each ${\gamma }_j$ is a hyperbolic geodesic in $(\hat{\mathbb{C}}\setminus \gamma )\cup {\gamma }_j$.…