7 papers
Quasilinear Liouville equation on manifolds with nonnegative Ricci curvature
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
We prove rigidity and classification results for the quasilinear Liouville equation associated with the -Laplacian on complete noncompact Riemannian manifolds with nonnegative R…
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…
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 splittin…
Rigidity for the heat equation with density on Riemannian manifolds through a conformal change
Alexander Grigor'yan, Giulia Meglioli, Alberto Roncoroni
We investigate uniqueness of solution to the heat equation with a density on complete, non-compact weighted Riemannian manifolds of infinite volume. Our main goal is to identi…
Rigidity of solutions to singular/degenerate semilinear critical equations
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in , with…
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…