Space of chord-arc curves and BMO/VMO Teichmüller space

Authors

  • Katsuhiko Matsuzaki Waseda University, School of Education, Department of Mathematics
  • Huaying Wei Jiangsu Normal University, Department of Mathematics and Statistics; and Waseda University, School of Education, Department of Mathematics

Keywords:

Chord-arc curve, BMO Teichmüller space, VMO Teichmüller space, strongly quasisymmetric, strongly symmetric, Carleson measure, quotient Bers embedding, asymptotic Teichmüller space

Abstract

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.
Section
Articles

Published

2022-10-17

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