Platonic surfaces | Zendy

Robert Brooks | Zendy

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Platonic surfaces

Author(s) -

Robert Brooks

Publication year - 1999

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050082

Subject(s) - mathematics , conformal map , compactification (mathematics) , riemann surface , compact riemann surface , pure mathematics , constant curvature , lambda , curvature , mathematical analysis , geometry , physics , quantum mechanics

. 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.

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