Abstract
The Universal Teichmüller Space has recently gained the attention of physicists as a setting for developing string theory. Two common models for this space are the set of quasicircles and the set of quasisymmetries. The link between these models lies in the fact that the Riemann maps from \(\mathbb{D}\) and \(\mathbb{D}^*\) to the complementary domains of quasicircles induce quasisymmetric automorphisms of \(\partial \mathbb{D}\). We develop a means of approximating these quasisymmetries given their associated quasicircles. This provides a concrete method for switching from the quasicircle to the quasisymmetry model of the Universal Teichmüller Space. Our approach uses discrete analytic functions induced by circle packings to approximate the Riemann maps.
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Received May 19, 1999, and in revised form April 6, 2000. Online publication September 22, 2000.
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Brock Williams, G. Approximation of Quasisymmetries Using Circle Packings. Discrete Comput Geom 25, 103–124 (2001). https://doi.org/10.1007/s004540010067
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DOI: https://doi.org/10.1007/s004540010067