Accessory parameters for punctured spheres

Source abstract

This paper contains some qualitative results about the accessory parameters for punctured spheres with signature. We show that the Fuchsian uniformizing connection, and hence also the accessory parameters, for the surface depends real analytically on moduli. We also show that the important invariants of a uniformization of a punctured sphere such as the accessory parameters, Fuchsian groups, Poincaré metrics, and covering maps vary continuously under degenerations such as coalescing of punctures.