The Liouville equation on Riemannian surfaces: the role of volume growth in classification and rigidity results

Giulio Ciraolo, Alberto Farina, Michele Gatti

We study the Liouville equation $-\Delta u=e^u$ on a complete, connected, non-compact, boundaryless Riemannian surface $(M,g)$ with non-negative Ricci curvature. Assuming only some as…