Conformal and cp types of surfaces of class $\mathcal{S}$

TL;DR

This paper investigates the relationship between the conformal type and circle packing type of Riemann surfaces of class $\

Contribution

It introduces a method to define the circle packing type for surfaces of class $\

Findings

Defines cp parabolic and hyperbolic types for surfaces of class $\

Establishes relations between conformal and circle packing types

Abstract

In this paper we describe how to define the circle packing (cp) type(either cp parabolic or cp hyperbolic) of a Riemann surface of class $\mathcal{S}$, and study the relation between this type and the conformal type of the surface.