JournalscmhVol. 74 , No. 1DOI 10.1007/s000140050082

Platonic surface

  • R. Brooks

    Technion - Israel Institute of Technology, Haifa, Israel
Platonic surface cover

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.