A note on mean field type equations

Abstract

In this article, we provide a note on rigidity results for mean field-type equations with multiple exponential terms, including sinh-Gordon and Tzitzeica equations, on closed two-dimensional manifolds with positive Ricci curvature bounds. It is based on two nonlinear transformations and a geometric identity developed by Dolbeault et al.

Keywords

• rigidity
• mean field equations
• geometric identity
• nonlinear transformations
• sinh-gordon
• 35j20
• 35j60
• 49s05