Geodesic
Space of chord-arc curves and BMO/VMO Teichmüller space
Katsuhiko Matsuzaki1 ; Huaying Wei2
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
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 27-42.

Voir la notice de l'article provenant de la source Journal.fi

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.
DOI : 10.54330/afm.122367
Keywords: Chord-arc curve, BMO Teichmüller space, VMO Teichmüller space, strongly quasisymmetric, strongly symmetric, Carleson measure, quotient Bers embedding, asymptotic Teichmüller space

Katsuhiko Matsuzaki 1 ; Huaying Wei 2

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 
@article{AFM_2023_48_1_a1,
     author = {Katsuhiko Matsuzaki and Huaying Wei},
     title = {Space of chord-arc curves and {BMO/VMO} {Teichm\"uller} space},
     journal = {Annales Fennici Mathematici},
     pages = {27--42},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2023},
     doi = {10.54330/afm.122367},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.122367/}
}
TY  - JOUR
AU  - Katsuhiko Matsuzaki
AU  - Huaying Wei
TI  - Space of chord-arc curves and BMO/VMO Teichmüller space
JO  - Annales Fennici Mathematici
PY  - 2023
SP  - 27
EP  - 42
VL  - 48
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.122367/
DO  - 10.54330/afm.122367
LA  - en
ID  - AFM_2023_48_1_a1
ER  - 
%0 Journal Article
%A Katsuhiko Matsuzaki
%A Huaying Wei
%T Space of chord-arc curves and BMO/VMO Teichmüller space
%J Annales Fennici Mathematici
%D 2023
%P 27-42
%V 48
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.122367/
%R 10.54330/afm.122367
%G en
%F AFM_2023_48_1_a1
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. http://geodesic.mathdoc.fr/articles/10.54330/afm.122367/

Cité par Sources :