If SO is a Riemann surface with a complete metric of finite area and constant curvature -1, let SC denote the conformal compactification of SO. We show that, under the assumption that the cusps of SO are large, there is a close relationship between the hyperbolic metrics on SO and SC. We use this relationship to show that , where the Platonic surface Pk is the conformal compactification of the modular surface Sk.
Cite this article
R. Brooks, Platonic surface. Comment. Math. Helv. 74 (1999), no. 1, pp. 156–170DOI 10.1007/S000140050082