In this talk I will present some recent results on the Kirchhoff equation of nonlinear elasticity, describing transversal oscillations of strings and plates, with periodic boundary conditions. We are...
The Kuramoto model is a nonlinear system of ODEs that represents the behavior of coupled oscillators. The coupling is determined by a given graph and pushes the system towards synchronization. An impo...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
In the last years there has been a renewed interest around a long-standing conjecture by Griffiths characterizing which should be the positive characteristic forms for any Griffiths positive vector bu...
I shall consider elliptic problems addressing the study of the geometric properties of the solutions. This issue is in general related to the classification of the solutions or to Liouville type theor...
Building on the introduction to spin geometry taught by Bernhard Hanke, I will use spinorial methods to investigate manifolds whose scalar curvature satisfies restrictions. Scalar curvature contains m...
Spin geometry arises from the attempt to define a first-order differential operator whose square is equal to the Laplace operator. In Euclidean space this problem can be solved after moving from scala...
We shall show that a Riemanian manifold whose sectional curvature is strictly between 1 and 1/4 is diffeomorphic to the standard sphere. The proof uses the Ricci flow without surgery and a nice work o...
We shall show that a Riemanian manifold whose sectional curvature is strictly between 1 and 1/4 is diffeomorphic to the standard sphere. The proof uses the Ricci flow without surgery and a nice work o...
In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. ...
