In these lectures we will describe the relationship between
optimal transportation and nonlinear elliptic PDE of Monge-Ampere
type, focusing on recent advances in characterizing costs and
domains for which the Monge-Kantorovich problem has smooth...
We will discuss topological information carried by weakly
differentiable maps and its applications in an existence theory for
absolute minimizers of the Faddeev knot energies in higher
dimensions.
I will discuss how some questions in conformal geometry can be
answered using twistor theory. One such application is to the
classification of locally conformally flat Hermitian surfaces.
Another application is to determining the conformal...
We consider the problem of finding complete conformal metrics
determined by a symmetric function of Ricci tensor in a negative
convex cone on compact manifolds. A consequence of our main results
is that any smooth bounded domain in Euclidean space...
After recalling the definition of $Q$-curvature and some
applications, we will address the question of prescribing it
through a conformal deformation of the metric. We will address some
compactness issues, treated via blow-up analysis, and then...
We discuss Einstein-scalar field Lichnerowicz equations on
compact Riemannian manifolds from the viewpoint of existence
results and stability issues. We prove that the Einstein-scalar
field Lichnerowicz equation is stable when $n \le 5$, and...
After recalling the definition of $Q$-curvature and some
applications, we will address the question of prescribing it
through a conformal deformation of the metric. We will address some
compactness issues, treated via blow-up analysis, and then...
The goal of this course to provide an introduction to
Monge-Ampere-type equations in conformal geometry and their
applications. The plan of the course is the following: After
providing some background material in conformal geometry, I will
describe...
We will discuss the introduction of the scattering operators
associated with a conformal manifold by Graham and Zworski. Then we
will discuss some uses of such family of operators in describing
conformally invariant global quantities for conformal...
The goal of this course to provide an introduction to
Monge-Ampere-type equations in conformal geometry and their
applications. The plan of the course is the following: After
providing some background material in conformal geometry, I will
describe...
