105 citations · 248 across the 46 of their papers we have counts for
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A remark on compact hypersurfaces with constant mean curvature in space forms
Giovanni Catino
In this note we characterize compact hypersurfaces of dimension with constant mean curvature immersed in space forms of constant curvature and satisfying an optimal i…
On conformally flat manifolds with constant positive scalar curvature
Giovanni Catino
We classify compact conformally flat -dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isome…
A variational characterization of flat spaces in dimension three
Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli
In this short note we prove that, in dimension three, flat metrics are the only complete metrics with non-negative scalar curvature which are critical for the -curvature fun…
Conformal Ricci Solitons and related Integrability Conditions
Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli +1
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds an…
Some rigidity results on critical metrics for quadratic functionals
Giovanni Catino
In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics wi…
Analytic and geometric properties of generic Ricci solitons
Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli +1
The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soli…