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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Horocycles on Riemann surfaces


Authors: Mika Seppälä and Tuomas Sorvali
Journal: Proc. Amer. Math. Soc. 118 (1993), 109-111
MSC: Primary 30F45; Secondary 51M10, 53A35
MathSciNet review: 1128730
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Abstract: By the Collar Theorem, every puncture on a hyperbolic Riemann surface with punctures has a horocyclic neighborhood of area $ 2$. Furthermore two such neighborhoods associated to different punctures are disjoint.

This result can be improved if we omit the condition that horocyclic neighborhoods of different punctures must be disjoint. Using arguments of the second author we show, in this paper, that each puncture of a hyperbolic Riemann surface has a horocyclic neighborhood of area $ 4$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1128730-3
PII: S 0002-9939(1993)1128730-3
Article copyright: © Copyright 1993 American Mathematical Society