Conformal mappings of a once-holed torus
\textit{M. Shiba} showed [Trans. Am. Math. Soc. 301, 299-311 (1987; Zbl 0626.30046)] that the set of moduli of marked tori into which a given marked open Riemann surface can be embedded is precisely a closed disk in the upper half plane. The author uses this result to solve the problem whether a once-holed torus can be conformally embedded into another or not. Moreover, he gives a new set of moduli for the Teichmüller space of a once-holed torus and describes the action of the modular group on the Teichmüller space. The problem to relate the new set of moduli to ones introduced before seems to be difficult.
scientific article; zbMATH DE number 854439
scientific article