Topological Regularity for Solutions to the Generalised Hopf Equation
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Date
2023-08-02
Open Access Location
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Rights
(c) 2023 The Author/s
CC BY 4.0
CC BY 4.0
Abstract
The 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.
Description
Keywords
Harmonic mapping, Hopf equation, Finite distortion, Partial differential equations, Topological regularity
Citation
Martin G, Yao C. (2023). Topological Regularity for Solutions to the Generalised Hopf Equation. Complex Analysis and Operator Theory. 17. 6.