Accepted Paper

Inserted: 6 nov 2025
Last Updated: 8 apr 2026

Journal: J. Math. Anal. Appl.
Year: 2026

Abstract:

The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow with non-negative weight functions on 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.