105 citations · 248 across the 46 of their papers we have counts for
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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…
Rigidity of positively curved shrinking Ricci solitons in dimension four
Giovanni Catino
We classify four-dimensional shrinking Ricci solitons satisfying , where and denote the sectional and the scalar curvature, respectively. They ar…
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…
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…