Platonic surface

  • R. Brooks

    Technion - Israel Institute of Technology, Haifa, Israel

Abstract

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 lim infkλ1(Pk)5/36\liminf_{k \to \infty} \lambda_1(P_k) \ge 5/36, 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. 156–170

DOI 10.1007/S000140050082