Abstract
We give an easy description of the barycentric extension of a map of the unit circle to the closed unit disk using some ideas from dynamical systems. We then prove that every circle endomorphism of the unit circle of degree d ≥ 2 (with a topological expansion condition) has a conformally natural extension to the closed unit disk which is real analytic on the open unit disk. If the endomorphism is uniformly quasisymmetric, then the extension is quasiconformal.
Citation
Yunping Jiang. Sudeb Mitra. Zhe Wang. "Conformally natural extensions in view of dynamics." Kodai Math. J. 36 (1) 167 - 173, March 2013. https://doi.org/10.2996/kmj/1364562727
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