Space of chord-arc curves and BMO/VMO Teichmüller space
Keywords:Chord-arc curve, BMO Teichmüller space, VMO Teichmüller space, strongly quasisymmetric, strongly symmetric, Carleson measure, quotient Bers embedding, asymptotic Teichmüller space
AbstractThis 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.
How to Cite
Matsuzaki, K., & Wei, H. (2022). Space of chord-arc curves and BMO/VMO Teichmüller space. Annales Fennici Mathematici, 48(1), 27–42. https://doi.org/10.54330/afm.122367
Copyright (c) 2022 Annales Fennici Mathematici
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.