@inproceedings{adrien1985conformally,
title={Conformally natural extension of homeomorphisms of the circle},
author={Adrien Douady, and Clifford J. Earle},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203306761280388},
booktitle={Acta Mathematica},
volume={157},
number={1},
pages={23-48},
year={1985},
}
Adrien Douady, and Clifford J. Earle. Conformally natural extension of homeomorphisms of the circle. 1985. Vol. 157. In Acta Mathematica. pp.23-48. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203306761280388.