Estimates of the hyperbolic metric on the twice punctured plane

Kim, Seong-A; Ma, Jianjun; Ma, W.

doi:10.5186/aasfm.2015.4058

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“…Many authors have studied these topics which bring together extremal problems of geometric function theory, classical hyperbolic geometry, special classes of domains, metric structure conditions of sets, and special functions [3,2,9,10,11,17,15,18,19,21,22,23,27,30,35]. Mostly, the density function of the distance is studied.…”

Section: Introductionmentioning

confidence: 99%

Construction of nearly hyperbolic distance on punctured spheres

Sugawa

Zhang²

2017

Bull. Math. Sci.

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We define a distance function on the bordered punctured disk 0 < |z| ≤ 1/e in the complex plane, which is comparable with the hyperbolic distance of the punctured unit disk 0 < |z| < 1. As an application, we will construct a distance function on an n-times punctured sphere which is comparable with the hyperbolic distance. We also propose a comparable quantity which is not necessarily a distance function on the punctured sphere but easier to compute.

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