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arXiv · 2511.03624

Critical sinh-Gordon flow with non-negative weight functions

Qiang Fei·Aleks Jevnikar·Sang-Hyuck Moon
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Abstract

The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow \begin{equation*} {\frac{\partial}{\partial t}}e^u=Δ_gu+8π\left({\frac{h_1e^u}{\int_Σh_1e^udV_g}}-1\right)-ρ_2\left({\frac{h_2e^{-u}}{\int_Σh_2e^{-u}dV_g}}-1\right), \end{equation*} where $ρ_2<8π$, $h_1,h_2$ are non-negative weight functions and $Σ$ is a closed Riemannian surface. Secondly, under suitable geometric conditions, we prove the convergence of the flow to a solution of the critical sinh-Gordon equation, extending the result of Zhou (2008) to the case of non-negative weights. The argument is based on a careful blow-up analysis. Some remarks about a Toda flow are also given.

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Qiang Fei, Aleks Jevnikar, Sang-Hyuck Moon. 2025-11-05. Critical sinh-Gordon flow with non-negative weight functions. https://doi.org/10.1016/j.jmaa.2026.130682

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