On quasisymmetry of quasiconformal mappings

M. Huang; S. Ponnusamy; A. Rasila; X. Wang

doi:10.1016/j.aim.2015.09.036

On quasisymmetry of quasiconformal mappings

M. Huang, S. Ponnusamy, A. Rasila, X. Wang^*

^*Corresponding author for this work

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

12 Scopus citations

Abstract

Suppose that f:D→D^' is a quasiconformal mapping, where D and D^' are domains in Rn, and that D is a broad domain. We show that for every arcwise connected subset A in D, the weak quasisymmetry of the restriction f|A: A→f(A) implies its quasisymmetry. As a consequence, we see that the answer to one of the open problems raised by Heinonen from 1989 is affirmative, under the additional condition that A is arcwise connected.

Original language	English
Pages (from-to)	1069-1096
Number of pages	28
Journal	Advances in Mathematics
Volume	288
DOIs	https://doi.org/10.1016/j.aim.2015.09.036
State	Published - 22 Jan 2016
Externally published	Yes

Keywords

Broad domain
LLC set
Quasiconformal mapping
Quasisymmetry
Weak quasisymmetry

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10.1016/j.aim.2015.09.036

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abstract = "Suppose that f:D→D' is a quasiconformal mapping, where D and D' are domains in Rn, and that D is a broad domain. We show that for every arcwise connected subset A in D, the weak quasisymmetry of the restriction f|A: A→f(A) implies its quasisymmetry. As a consequence, we see that the answer to one of the open problems raised by Heinonen from 1989 is affirmative, under the additional condition that A is arcwise connected.",

keywords = "Broad domain, LLC set, Quasiconformal mapping, Quasisymmetry, Weak quasisymmetry",

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T1 - On quasisymmetry of quasiconformal mappings

AU - Huang, M.

AU - Ponnusamy, S.

AU - Rasila, A.

AU - Wang, X.

PY - 2016/1/22

Y1 - 2016/1/22

N2 - Suppose that f:D→D' is a quasiconformal mapping, where D and D' are domains in Rn, and that D is a broad domain. We show that for every arcwise connected subset A in D, the weak quasisymmetry of the restriction f|A: A→f(A) implies its quasisymmetry. As a consequence, we see that the answer to one of the open problems raised by Heinonen from 1989 is affirmative, under the additional condition that A is arcwise connected.

AB - Suppose that f:D→D' is a quasiconformal mapping, where D and D' are domains in Rn, and that D is a broad domain. We show that for every arcwise connected subset A in D, the weak quasisymmetry of the restriction f|A: A→f(A) implies its quasisymmetry. As a consequence, we see that the answer to one of the open problems raised by Heinonen from 1989 is affirmative, under the additional condition that A is arcwise connected.

KW - Broad domain

KW - LLC set

KW - Quasiconformal mapping

KW - Quasisymmetry

KW - Weak quasisymmetry

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DO - 10.1016/j.aim.2015.09.036

M3 - 文章

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SN - 0001-8708

VL - 288

SP - 1069

EP - 1096

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

On quasisymmetry of quasiconformal mappings

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Keywords

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