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On the area growth of a hyperbolic surface
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1989