Luciano Mari

Professore/Professoressa associato/a

Curriculum Vitae (0.1 MB)

Complementi di Geometria (MAT0183 )
Laurea magistrale in Matematica
Curvature and topology in Riemannian Geometry
PhD in Pure and Applied Mathematics
Geometria e Algebra Lineare I A (MFN1308)
Corso di laurea in Fisica

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.