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arXiv · 1607.06310

Continuity of the barycentric extension of circle diffeomorphisms of Hölder continuous derivatives

Katsuhiko Matsuzaki
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Abstract

The barycentric extension due to Douady and Earle gives a conformally natural extension of a quasisymmetric automorphism of the circle to a quasiconformal automorphism of the unit disk. We consider such extensions for circle diffeomorphisms of Hölder continuous derivatives and show that this operation is continuous with respect to an appropriate topology for the space of the corresponding Beltrami coefficients.

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Katsuhiko Matsuzaki. 2016-07-21. Continuity of the barycentric extension of circle diffeomorphisms of Hölder continuous derivatives. https://doi.org/10.1112/tlm3.12006

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