3 papers
math.AP2026
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 on a complete, connected, non-compact, boundaryless Riemannian surface with non-negative Ricci curvature. Assuming only some as…
math.AP2025
Rigidity of weighted manifolds via classification results for semilinear equations
Giulio Ciraolo, Alberto Farina, Troy Petitt
We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-Émery Ricci curvature. Our main goal is to classify positive s…
math.AP2024
Classification results, rigidity theorems and semilinear PDEs on Riemannian manifolds: a P-function approach
Giulio Ciraolo, Alberto Farina, Camilla Chiara Polvara
We consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds and study their classification as well as the effect of their presence on th…