Critical sinh-Gordon flow with non-negative weight functions

2025/11/05 by Fei, Qiang, Jevnikar, Aleks, Moon, Sang-Hyuck
#35J20 #35J61 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.03624

Abstract

The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow (∂)/(∂ t)e^u=Δ_gu+8π((h₁e^u)/(∫_Σh₁e^udV_g)-1)-ρ₂(\frach₂e^-u∫_Σh₂e^-udV_g-1), where ρ₂<8π, h₁,h₂ 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.

Citations

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• Another remark on a result of Ding-Jost-Li-Wang