Hyperbolic lengths of geodesics surrounding two punctures
Authors: Joachim A. Hempel and Simon J. Smith
Journal: Proc. Amer. Math. Soc. 103 (1988), 513-516
MSC: Primary 30C99; Secondary 51M10
MathSciNet review: 943076
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Abstract: For the plane regions with , and with , we describe, as , the hyperbolic lengths of the geodesies surrounding 0 and 1. Upper and lower bounds for the lengths are also stated, and these results are used to obtain inequalities, which are precise in a certain sense, for the length of the geodesic surrounding 0 and 1 in an arbitrary plane region satisfying .