Platonic surfaces |
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| Authors: | R Brooks |
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| Institution: | (1) Department of Mathematics, The Technion — Israel Institute of Technology, Haifa, Israel, e-mail: rbrooks@tx.technion.ac.il, IL |
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| Abstract: | If S
O is a Riemann surface with a complete metric of finite area and constant curvature -1, let S
C denote the conformal compactification of S
O. We show that, under the assumption that the cusps of S
O are large, there is a close relationship between the hyperbolic metrics on S
O and S
C. We use this relationship to show that , where the Platonic surface P
k is the conformal compactification of the modular surface S
k.
Received: November, 1996; revised: February, 1998 |
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| Keywords: | , Eigenvalue, Riemann surface, Ahlfors-Schwarz Lemma, |
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