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On the area growth of a hyperbolic surface

Published online by Cambridge University Press:  17 April 2009

Pui-Fai Leung
Pui-Fai Leung
Affiliation:
Department of MathematicsNational University of Singapore10 Kent Ridge CrescentSingapore 0511
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Abstract

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We conjecture that if the rate of area growth of a geodesic disc of radius r on a smooth simply-connected complete surface with non-positive Gaussian curvature is faster than r2(logr)1+e for some ε ≥ 0, then the surface is hyperbolic. We prove this under an additional assumption that the surface is rotationally symmetric.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 435 - 438
Copyright
Copyright © Australian Mathematical Society 1989

References

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