Continuity of the barycentric extension of circle diffeomorphisms with Hölder continuous derivative

Katsuhiko Matsuzaki

doi:10.1112/tlm3.12006

Continuity of the barycentric extension of circle diffeomorphisms with Hölder continuous derivative

Katsuhiko Matsuzaki^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	129-147
Number of pages	19
Journal	Transactions of the London Mathematical Society
Volume	4
Issue number	1
DOIs	https://doi.org/10.1112/tlm3.12006
Publication status	Published - 2017 Dec 1

Keywords

30C62 (primary)
30F60
37E30 (secondary)

ASJC Scopus subject areas

Mathematics(all)

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10.1112/tlm3.12006

Cite this

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abstract = "The barycentric extension due to Douady and Earle yields a conformally natural extension of a quasisymmetric self-homeomorphism of the unit circle to a quasiconformal self-homeomorphism of the unit disk. We consider such extensions for circle diffeomorphisms with H{\"o}lder continuous derivative 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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KW - 30F60

KW - 37E30 (secondary)

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Continuity of the barycentric extension of circle diffeomorphisms with Hölder continuous derivative

Abstract

Keywords

ASJC Scopus subject areas

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