Martin GYao C2024-07-312024-07-312023-08-02Martin G, Yao C. (2023). Topological Regularity for Solutions to the Generalised Hopf Equation. Complex Analysis and Operator Theory. 17. 6.1661-8254https://mro.massey.ac.nz/handle/10179/71174The generalised Hopf equation is the first order nonlinear equation defined on a planar domain Ω ⊂ C , with data Φ a holomorphic function and η≥ 1 a positive weight on Ω , hwhw¯¯η(w)=Φ. The Hopf equation is the special case η(w) = η~ (h(w)) and reflects that h is harmonic with respect to the conformal metric η~(z)|dz| , usually η is the hyperbolic metric. This article obtains conditions on the data to ensure that a solution is open and discrete. We also prove a strong uniqueness result.(c) 2023 The Author/sCC BY 4.0https://creativecommons.org/licenses/by/4.0/Harmonic mappingHopf equationFinite distortionPartial differential equationsTopological regularityJournal article10.1007/s11785-023-01390-41661-8262journal-article91