Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

Katsuhiko Matsuzaki*

*この研究の対応する著者

研究成果査読

3 被引用数 (Scopus)

抄録

Based on the quasiconformal theory of the universal Teichmüller space, we introduce the Teichmüller space of diffeomorphisms of the unit circle with α-Hölder continuous derivatives as a subspace of the universal Teichmüller space. We characterize such a diffeomorphism quantitatively in terms of the complex dilatation of its quasiconformal extension and the Schwarzian derivative given by the Bers embedding. Then, we provide a complex Banach manifold structure for it and prove that its topology coincides with the one induced by local C1+α-topology at the base point.

本文言語English
ページ(範囲)1333-1374
ページ数42
ジャーナルRevista Matematica Iberoamericana
36
5
DOI
出版ステータスPublished - 2020 2 10

ASJC Scopus subject areas

  • 数学 (全般)

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