Dott. Luciano Mari
- Department of Mathematics "Giuseppe Peano"
- SSD: MAT/03 - geometry
My research lies in the field of Geometric Analysis, in particular I worked on the following topics:
- maximum principles at infinity on Riemannian manifolds, relations to (fully)nonlinear potential theory, and geometric applications;
- Yamabe type problems (prescribed scalar curvature problems) on noncompact manifolds;
- Positive energy theorems in General Relativity;
- Geometry of minimal submanifolds, especially of dimension higher than 2;
- Spectrum of the Laplace-Beltrami operators on Riemannian manifolds, with emphasis on immersed submanifolds with bounded mean curvature;
- Mean curvature flow and inverse mean curvature flow;
- Mean curvature operators and the geometry of entire graphs with prescribed mean curvature, with emphasis on capillary and minimal ones;
- Overdetermined elliptic problems;
- The Lorentzian mean curvature equation and the Born-Infeld model.