The rate of convergence of the hyperbolic density on sequences of domains

Nikola Lakic; Greg Markowsky

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arXiv · 1210.1619

The rate of convergence of the hyperbolic density on sequences of domains

Nikola Lakic·Greg Markowsky

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Abstract

It is known that if a sequence of domains $U_n$ converges to a domain $U$ in the Caratheodory sense then the hyperbolic densities on $U_n$ converge to the hyperbolic density on $U$. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmueller density and the three-point density. We obtain several results which give rates of convergence in various scenarios.

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Nikola Lakic, Greg Markowsky. 2012-10-05. The rate of convergence of the hyperbolic density on sequences of domains. https://arxiv.org/abs/1210.1619

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