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The Discrete Schwarz-Pick Lemma for Overlapping Circles

1994
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Proceedings of the American Mathematical Society
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Let P and P' be circle packings in the hyperbolic plane such that they are combinatorically equivalent, neighboring circles in P overlap one another at some fixed angle between 0 and n/2 and the corresponding pairs of circles in P' overlap at the same angle, and the radius for any boundary circle of P is less than or equal to that of the corresponding boundary circle of P'. In this paper we show that the radius of any interior circle of P is less than or equal to that of the corresponding

doi:10.2307/2161218
fatcat:zntk3gm64fgrlk6rcpqql4xnrm