Geodesic
Characterizations of circle homeomorphisms of different regularities in the universal Teichmüller space
Jun Hu1
1Brooklyn College of CUNY, Brooklyn, USA
EMS surveys in mathematical sciences, Tome 9 (2022) no. 2, pp. 321-353

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DOI

In this survey, we first give a summary of characterizations of circle homeomorphisms of different regularities (quasisymmetric, symmetric, or C1+α) in terms of Beurling–Ahlfors extension, Douady–Earle extension, and Thurston's earthquake representation of an orientation-preserving circle homeomorphism. Then we provide a brief account of characterizations of the elements of the tangent spaces of these sub-Teichmüller spaces at the base point in the universal Teichmüuller space.
DOI : 10.4171/emss/60
Classification : 30-XX
Mots-clés : Beurling–Ahlfors extension, Douady–Earle extension, Thurston's earthquake map, quasiconformal map, Zygmund-bounded function, Hölder continuity, Teichmüller space, little Teichmüller space

Jun Hu  1

1 Brooklyn College of CUNY, Brooklyn, USA 
Jun Hu. Characterizations of circle homeomorphisms of different regularities in the universal Teichmüller space. EMS surveys in mathematical sciences, Tome 9 (2022) no. 2, pp. 321-353. doi: 10.4171/emss/60
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     title = {Characterizations of circle homeomorphisms of different regularities in the universal {Teichm\"uller} space},
     journal = {EMS surveys in mathematical sciences},
     pages = {321--353},
     year = {2022},
     volume = {9},
     number = {2},
     doi = {10.4171/emss/60},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/60/}
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