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Quasiconformal homogeneity and subgroups of the mapping class group. (English) Zbl 1319.30012

Motivated by the work of Bonfert-Taylor, Bridgeman, Canary, and Taylor, the author studies closed oriented hyperbolic surfaces and defines the notion of quasiconformal homogeneity restricted to subgroups of the mapping class group. The author gives lower bounds for the associated quasiconformal homogeneity constants in several cases such as the Torelli group, congruence subgroups, and pure cyclic subgroups. The lower bounds are given in terms of the parameters and the modulus of the Grötzsch ring domain. For related recent results see [P. Bonfert-Taylor et al., Comput. Methods Funct. Theory 14, No. 2–3, 417–430 (2014; Zbl 1307.30051)].

MSC:

30C62 Quasiconformal mappings in the complex plane
30F45 Conformal metrics (hyperbolic, Poincaré, distance functions)

Citations:

Zbl 1307.30051
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References:

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