The subvarieties in Shottkys space and the two-generated groups of conformal automorphismes

In this work topological and analytical properties of subvarieties in Teichmüllers space $\mathbb{T}_h$, consisting of marked compact Riemann surfaces of genus $h\geqslant2$, which admit special two-generated groupes of conformal automorphismes and propeties of subvarieties in Shottkys space associating to it are studied. For this purpose are considered two cases of special two-generated groupes of conformal automorphismes on marked compact Riemann surface.