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

 

Complete metrics conformal to the hyperbolic disc


Authors: J. Bland and Morris Kalka
Journal: Proc. Amer. Math. Soc. 97 (1986), 128-132
MSC: Primary 53A30; Secondary 35J15, 58G30
MathSciNet review: 831400
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Abstract: In this paper we study complete metrics conformal to the hyperbolic disc. We show that any smooth function $ K$ bounded between two negative constants is the curvature of such a metric. We also show that if $ K \geq 0$ near the boundary, $ K$ cannot be the curvature of such a metric.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0831400-6
PII: S 0002-9939(1986)0831400-6
Article copyright: © Copyright 1986 American Mathematical Society