While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic dilfeomorphisms. 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 Omega* there exists a epsilon> 0 such that for every doubly connected domain Omega with Mod Omega* < Mod Omega < Mod Omega* + epsilon th...
