Quasiconformal homogeneity and subgroups of the mapping class group
arXiv:1309.7026 · doi:10.2140/agt.2015.15.1909
Abstract
In the vein of Bonfert-Taylor, Bridgeman, Canary, and Taylor we introduce the notion of quasiconformal homogeneity for closed oriented hyperbolic surfaces restricted to subgroups of the mapping class group. We find uniform lower bounds for the associated quasiconformal homogeneity constants across all closed hyperbolic surfaces in several cases, including the Torelli group, congruence subgroups, and pure cyclic subgroups. Further, we introduce a counting argument providing a possible path to exploring a uniform lower bound for the nonrestricted quasiconformal homogeneity constant across all closed hyperbolic surfaces.
26 pages, 2 figures. This version incorporates referee's comments and has been accepted for publication in the Michigan Mathematical Journal