Topological regularity for solutions to the generalised Hopf equation

2023/04/28 by Martin, Gaven, Yao, Cong
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.14761

Abstract

The generalised Hopf equation is the first order nonlinear equation with data Φ a holomorphic functions and η≥ 1 a positive weight, h_w h_\wbar 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|. This article obtains conditions on the data to ensure that a solution is open and discrete. We also prove a strong uniqueness result.

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