Critical sinh-Gordon flow with non-negative weight functions
Abstract
The aim of this article is twofold: on one side we introduce and study the properties of a critical sinh-Gordon type flow ∂ ∂ t e u = Δ g u + 8 π ( h 1 e u ∫ Σ h 1 e u d V g − 1 ) − ρ 2 ( h 2 e − u ∫ Σ h 2 e − u d V g − 1 ) , where ρ 2 < 8 π , 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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 562
- Issue
- 1
- Pages
- 130682–130682
- Publication date
- 7 April 2026
- Language
- EN