5 papers
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…
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…
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.…