TY - JOUR
AU - Matsuzaki, Katsuhiko
AU - Wei, Huaying
PY - 2022/10/17
Y2 - 2022/11/27
TI - Space of chord-arc curves and BMO/VMO Teichmüller space
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 48
IS - 1
SE - Articles
DO - 10.54330/afm.122367
UR - https://afm.journal.fi/article/view/122367
SP - 27-42
AB - <pre>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.</pre>
ER -