25 citations · 48 across the 36 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
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…
The Poisson equation on manifolds with positive essential spectrum
Giovanni Catino, Dario Daniele Monticelli, Fabio Punzo
We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particu…
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…