8 papers
Conformal Kähler rigidity of Einstein four-manifolds
Giovanni Catino, Davide Dameno
For a compact, connected, oriented Einstein four-manifold, we prove that, if the largest eigenvalue of the self-dual Weyl curvature is everywhere simple, then, after at worst…
Quasilinear Liouville equation on manifolds with nonnegative Ricci curvature
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
We prove rigidity and classification results for the quasilinear Liouville equation associated with the -Laplacian on complete noncompact Riemannian manifolds with nonnegative R…
Gradient estimates for the Green kernel under spectral Ricci bounds, and the stable Bernstein theorem in
Xavier Cabre, Giovanni Catino, Luciano Mari +2
We describe a method to prove new integral inequalities for stable minimal hypersurfaces in Euclidean space. As an application, we give a simple proof that complete, two sided, sta…
Criticality, splitting theorems under spectral Ricci bounds and the topology of stable minimal hypersurfaces
Giovanni Catino, Luciano Mari, Paolo Mastrolia +1
In this paper we prove general criticality criteria for operators on manifolds with more than one end, where bounds the Ricci curvature, and a related spectral splittin…
Rigidity of solutions to singular/degenerate semilinear critical equations
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in , with…
Bach-pinched metrics on closed manifolds
Letizia Branca, Giovanni Catino, Davide Dameno
Exploiting the deformation method introduced by Aubin in his seminal work to construct constant negative scalar curvature metrics, we show the existence, on every closed manifold o…