Tessellations and Speiser graphs arising from meromorphic functions on simply connected Riemann surfaces

Alvaro Alvarez-Parrilla, Jesus Muciño-Raymundo

Motivated by W. P. Thurston, we ask: What is the shape of a meromorphic function on a simply connected Riemann surface ${\Omega }_z$? We consider Speiser functions, i.e. meromorphic functi…