1Waseda University, School of Education, Department of Mathematics 2Jiangsu Normal University, Department of Mathematics and Statistics; and Waseda University, School of Education, Department of Mathematics
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 27-42
This paper focuses on the structure of the subspace $T_c$ of the BMO Teichmüller space $T_b$ corresponding to chord-arc curves, which contains the VMO Teichmüller space $T_v$. We prove that $T_c$ is not a subgroup with respect to the group structure of $T_b$, but it is preserved under the inverse operation and the left and the right translations by any element of $T_v$. Moreover, we show that $T_b$ has a fiber structure induced by $T_v$, and the complex structure of $T_b$ can be projected down to the quotient space $T_v \backslash T_b$. Then, we see that $T_c$ consists of fibers of this projection, and its quotient space also has the induced complex structure.
1
Waseda University, School of Education, Department of Mathematics
2
Jiangsu Normal University, Department of Mathematics and Statistics; and Waseda University, School of Education, Department of Mathematics
Katsuhiko Matsuzaki; Huaying Wei. Space of chord-arc curves and BMO/VMO Teichmüller space. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 27-42. doi: 10.54330/afm.122367
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title = {Space of chord-arc curves and {BMO/VMO} {Teichm\"uller} space},
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