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arXiv · 1704.07954

Construction of nearly hyperbolic distance on punctured spheres

Toshiyuki Sugawa·Tanran Zhang
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Abstract

We define a distance function on the bordered punctured disk $0<|z|\le 1/e$ 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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Toshiyuki Sugawa, Tanran Zhang. 2017-04-26. Construction of nearly hyperbolic distance on punctured spheres. https://arxiv.org/abs/1704.07954

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