TY - JOUR

T1 - Non-existence of prescribable conformally equivariant dilatation in space

AU - Chaiya, Malinee

AU - Hinkkanen, Aimo

PY - 2013/8/27

Y1 - 2013/8/27

N2 - In this paper, we study the prescribable conformally equivariant dilatations for orientation preserving quasiconformal homeomorphisms. The complex dilatation is a prescribable conformally equivariant dilatation in ℝ2. A Schottky set is a subset of the unit sphere Sn whose complement is the union of at least three disjoint open balls. By using the result of Bonk, Kleiner, and Merenkov that there are rigid Schottky sets of positive measure in each dimension at least 3, we prove that it is not possible to have a prescribable conformally equivariant dilatation in ℝn, where n ≥ 3.

AB - In this paper, we study the prescribable conformally equivariant dilatations for orientation preserving quasiconformal homeomorphisms. The complex dilatation is a prescribable conformally equivariant dilatation in ℝ2. A Schottky set is a subset of the unit sphere Sn whose complement is the union of at least three disjoint open balls. By using the result of Bonk, Kleiner, and Merenkov that there are rigid Schottky sets of positive measure in each dimension at least 3, we prove that it is not possible to have a prescribable conformally equivariant dilatation in ℝn, where n ≥ 3.

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U2 - 10.1090/S0002-9939-2013-11692-8

DO - 10.1090/S0002-9939-2013-11692-8

M3 - Article

AN - SCOPUS:84882694071

SN - 0002-9939

VL - 141

SP - 3985

EP - 3995

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -