Inclusion relations between the Bers embeddings of Teichmüller spaces
In this paper the author considers infinite-dimensional Teichmüller spaces, that is, Teichmüller spaces of non-finitely generated Fuchsian groups. The author first introduces a notion of ``exceptional groups'', that are groups where there are additional symmetries of the space of integrable holomorphic differentails. He is able to classify all such groups and then uses this result to show that for non-exceptional groups the Fuchsian group is uniquely determined by its Bers' embedding. The proof uses Teichmüller theory and a theorem of \textit{V. Markovic} [``Biholomorphic maps between Teichmüller spaces'', Duke Math. J. 120, No. 2, 405--431 (2003; Zbl 1056.30046)].
scientific article; zbMATH DE number 2114395