On the Teichmüller–Nitsche Problem of T. Iwaniec, L.V. Kovalev, and J. Onninen

Abstract

In 2011, Iwaniec et al. [8] posed the following problem: For which values s,t,1<s,t<∞ , does there exist a harmonic homeomorphism f: T(s) → T(t) , where T(·) is a Teichmüller domain? In 2022, Bshouty et al. [3] solved this problem only for harmonic homeomorphisms f satisfying the symmetric property f(z¯) = f(z) ¯ . The purpose of this paper is two-fold: (a) to establish for a given s> 1 a necessary condition for the existence of harmonic homeomorphisms f: T(s) → T(t) , and (b) to test in view of our results Conjecture 1.4 loc. cit. regarding the moduli of doubly-connected domains related by harmonic homeomorphisms. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.