The circle pattern uniformization problem.


  • Armando Rodado Amaris Universidad de Los Lagos.
  • Gina Lusares Universidad de Valparaíso.


Uniformization problem, Riemann surfaces of genus two, Circle pattern uniformization problem


The existence of an explicit and canonical cell decomposition of the moduli space of closed Riemann surfaces of genus two shows that each Riemann surface of genus two can be parametrised by a 12-tuple of real numbers which corresponds to the  angle coordinates of a graph associated to the surface. This suggests a Circle Pattern Uniformization Problem that we have defined and solved for three classical Riemann surfaces of genus two. Although in general, finding the exact algebraic equations corresponding to a hyperbolic surface from angle coordinates is a hard problem, we prove that known numerical methods can be applied to find approximated equations of Riemann surfaces of genus two from their angle coordinates and graph data for a large family of Riemann surfaces of genus two.

Author Biography

Armando Rodado Amaris, Universidad de Los Lagos.

Departamento de Ciencias Exactas.


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How to Cite

A. Rodado Amaris and G. Lusares, “The circle pattern uniformization problem.”, Proyecciones (Antofagasta, On line), vol. 36, no. 3, pp. 397-422, Oct. 2017.




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