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 I > 0 such that for every doubly connected domain Ω with ModΩ∗ < ModΩ < ModΩ∗ I there exists a harmonic diffeomorphism from Ω onto Ω∗.
|Original language||English (US)|
|Number of pages||10|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - Jun 1 2018|
- 2010 Mathematics subject classification: Primary 31A05
- Secondary 58E20
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