10 papers · 1 filter
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…
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…
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…
Uniqueness of critical metrics for a quadratic curvature functional
Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli
In this paper we prove a new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functional : we sh…
Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni +1
In this paper we study positive solutions to the CR Yamabe equation in noncompact -dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that th…