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On the existence of harmonic mappings between doubly connected domains

Published online by Cambridge University Press:  22 April 2018

Leonid V. Kovalev
Affiliation:
Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, NY 13244, USA ([email protected])
Liulan Li
Affiliation:
Hengyang Normal University, Hengyang, Hunan 421002, People's Republic of China ([email protected])

Abstract

While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic diffeomorphisms. Intuitively, one expects their existence if the domain is not too thick compared to the codomain. We make this intuition precise by showing that for a Dini-smooth doubly connected domain Ω* there exists a ε > 0 such that for every doubly connected domain Ω with ModΩ* < ModΩ < ModΩ* + ε there exists a harmonic diffeomorphism from Ω onto Ω*.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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