On the area growth of a hyperbolic surface
1989 ◽
Vol 39
(3)
◽
pp. 435-438
Keyword(s):
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.
Keyword(s):
1985 ◽
Vol 100
◽
pp. 135-143
◽
1987 ◽
Vol 26
(3)
◽
pp. 513-519
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1960 ◽
Vol 82
(1)
◽
pp. 60-68
◽
2015 ◽
Vol 112
(41)
◽
pp. 12639-12644
◽
1986 ◽
Vol 38
(2)
◽
pp. 328-359
◽
2004 ◽
Vol 20
(6)
◽
pp. 961-964
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