Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 657-679
Waseda University, School of Education, Department of Mathematics
Shinjuku, Tokyo 169-8050, Japan; matsuzak 'at' waseda.jp
Abstract. The Bers embedding of the Teichmüller space is a homeomorphism into the Banach space of certain holomorphic automorphic forms. For a subspace of the universal Teichmüller space and its corresponding Banach subspace, we consider whether the Bers embedding can project down between their quotient spaces. If this is the case, it is called the quotient Bers embedding. Injectivity of the quotient Bers embedding is the main problem in this paper. Alternatively, we can describe this situation as the universal Teichmüller space having an affine foliated structure induced by this subspace. We give several examples of subspaces for which the injectivity holds true, including the Teichmüller space of circle diffeomorphisms with Hölder continuous derivative. As an application, the regularity of conjugation between representations of a Fuchsian group into the group of circle diffeomorphisms is investigated.
2010 Mathematics Subject Classification: Primary 30F60; Secondary 37E30.
Key words: Asymptotically conformal, Schwarzian derivative, Bers embedding, quasisymmetric homeomorphism, circle diffeomorphism, integrable Teichmüller space, asymptotic Teichmüller space.
Reference to this article: K. Matsuzaki: Injectivity of the quotient Bers embedding of Teichmüller spaces. Ann. Acad. Sci. Fenn. Math. 44 (2019), 657-679.
https://doi.org/10.5186/aasfm.2019.4449
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