6 papers · 1 filter
On the classification of capillary graphs in Euclidean and non-Euclidean spaces
Giulio Colombo, Alberto Farina, Marco Magliaro +2
We prove some rigidity and classification results for graphs with prescribed mean curvature and locally constant Dirichlet and Neumann data, for instance as they appear in capillar…
Harmonic maps from to and the rigidity of the Hopf fibration
Athanasios Georgakopoulos, Marco Magliaro, Luciano Mari +1
It was conjectured by Eells that the only harmonic maps are Hopf fibrations composed with conformal maps of . We support this conjecture by proving its valid…
On mean curvature flow solitons in the sphere
Marco Magliaro, Luciano Mari, Fernanda Roing +1
In this paper, we consider soliton solutions of the mean curvature flow in the unit sphere moving along the integral curves of the Hopf unit vector field. While such sol…
Sharp pinching theorems for complete submanifolds in the sphere
Marco Magliaro, Luciano Mari, Fernanda Roing +1
We prove that every complete, minimally immersed submanifold whose second fundamental form satisfies , is either totally geodesi…
On splitting complete manifolds via infinity harmonic functions
Damião J. Araújo, Marco Magliaro, Luciano Mari +1
In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-ne…
Recent rigidity results for graphs with prescribed mean curvature
Bruno Bianchini, Giulio Colombo, Marco Magliaro +3
This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs . Emphasis is put on mi…