Non-existence of prescribable conformally equivariant dilatation in space

Malinee Chaiya, Aimo Hinkkanen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3985-3995
Number of pages11
JournalProceedings of the American Mathematical Society
Volume141
Issue number11
DOIs
StatePublished - Aug 27 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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