25 citations · 79 across the 24 of their papers we have counts for
30 papers
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…
On the Geometry of -Static Perfect Fluid Space-Times
Letizia Branca, Giulio Colombo, Paolo Mastrolia +2
In this paper we study the geometry of -static perfect fluid space-times (-SPFST, for short). In the context of Einstein's General Relativity, they arise from a space-time wh…
Some geometric properties of generalized -vacuum static spaces
Letizia Branca, Paolo Mastrolia, Marco Rigoli
In this paper we study the geometry of generalized -vacuum static spaces, proving estimates for the -scalar curvature and for the first eigenvalue of the Jacobi operator, and…
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 splitting…
Rigidity of Einstein manifolds with positive Yamabe invariant
Letizia Branca, Giovanni Catino, Davide Dameno +1
We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky…
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…
Two rigidity results for stable minimal hypersurfaces
Giovanni Catino, Paolo Mastrolia, Alberto Roncoroni
The aim of this paper is to prove two results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: we show that they are hyperplane in $\mathbb{…
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathb…
Some canonical metrics {\em via} Aubin's local deformations
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every compa…
Rigidity of Critical Metrics for Quadratic Curvature Functionals
Giovanni Catino, Paolo Mastrolia, Dario Daniele Monticelli
In this paper we prove new rigidity results for complete, possibly non-compact, critical metrics of the quadratic curvature functionals $\mathfrak{F}^{2}_t = \int |\operatorname{Ri…
On Riemannian four-manifolds and their twistor spaces: a moving frame approach
Giovanni Catino, Davide Dameno, Paolo Mastrolia
In this paper we study the twistor space of an oriented Riemannian four-manifold using the moving frame approach, focusing, in particular, on the Einstein, non-self-dual se…
A conformal Yamabe problem with potential on the euclidean space
Giovanni Catino, Filippo Gazzola, Paolo Mastrolia
We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally…
Four dimensional closed manifolds admit a weak harmonic Weyl metric
Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli +1
On four-dimensional closed manifolds we introduce a class of canonical Riemannian metrics, that we call weak harmonic Weyl metrics, defined as critical points in the conformal clas…
Weyl scalars on compact Ricci solitons
Giovanni Catino, Paolo Mastrolia
We investigate the triviality of compact Ricci solitons under general scalar conditions involving the Weyl tensor. More precisely, we show that a compact Ricci soliton is Einstein…
A potential generalization of some canonical Riemannian metrics
Giovanni Catino, Paolo Mastrolia
The aim of this paper is to study new classes of Riemannian manifolds endowed with a smooth potential function, including in a general framework classical canonical structures such…
Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds
Giovanni Catino, Paolo Mastrolia
The very definition of an Einstein metric implies that all its geometry is encoded in the Weyl tensor. With this in mind, in this paper we derive higher-order Bochner type formulas…
Gradient Ricci solitons with vanishing conditions on Weyl
Giovanni Catino, Paolo Mastrolia, Dario Daniele Monticelli
We classify complete gradient Ricci solitons satisfying a fourth-order vanishing condition on the Weyl tensor, improving previously known results. More precisely, we show that any…
Elliptic and parabolic equations with Dirichlet conditions at infinity on Riemannian manifolds
Paolo Mastrolia, Dario D. Monticelli, Fabio Punzo
We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in , where is a complete noncompact Riemann…
Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds
P. Mastrolia, D. D. Monticelli, F. Punzo
We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds.…
Classification of expanding and steady Ricci solitons with integral curvature decay
Giovanni Catino, Paolo Mastrolia, Dario Daniele Monticelli
In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assump…
Nonexistence results for elliptic differential inequalities with a potential on Riemannian manifolds
P. Mastrolia, D. D. Monticelli, F. Punzo
In this paper we are concerned with a class of elliptic differential inequalities with a potential both on $\erre^m$ and on Riemannian manifolds. In particular, we investigate the…
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…
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…