TY - JOUR
T1 - Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
This work was supported by JSPS KAKENHI 25287021.
Publisher Copyright:
© European Mathematical Society.
PY - 2020/2/10
Y1 - 2020/2/10
N2 - 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.
AB - 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.
KW - Beltrami coefficients
KW - Bers embedding
KW - Circle diffeomorphism
KW - Hölder continuous derivative
KW - Quasiconformal map
KW - Quasisymmetric homeomorphism
KW - Schwarzian derivative
KW - Universal Teichmüller space
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U2 - 10.4171/RMI/1169
DO - 10.4171/RMI/1169
M3 - Article
AN - SCOPUS:85084189736
VL - 36
SP - 1333
EP - 1374
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
SN - 0213-2230
IS - 5
ER -