Injectivity of the quotient Bers embedding of Teichmüller spaces

Katsuhiko Matsuzaki*

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)657-679
ページ数23
ジャーナルAnnales Academiae Scientiarum Fennicae Mathematica
44
2
DOI
出版ステータスPublished - 2019

ASJC Scopus subject areas

  • 数学 (全般)

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