# Recently Added

## Geometric PDE - Optimal Transportation and Nonlinear Elliptic PDE - Part I

## Geometric PDE - Optimal transportation and nonlinear elliptic PDE

http://www.math.ias.edu/sp/gpde

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 diffeomorphism solutions.

Background references.

L.C Evans, PDE and Monge-Kantorovich mass transfer. Current developments in Mathematics, 1997. Int. Press, Boston, (1999).

## Geometric PDE - Variational techniques for the prescribed Q-curvature equation

http://www.math.ias.edu/sp/gpde

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 study the problem, which has variational structure, using a Morse-theoretical approach.

## Geometric PDE - Variational techniques for the prescribed Q-curvature equation - Part II

## Geometric PDE - Variational techniques for the prescribed Q-curvature equation - Part I

## Geometric PDE - Fully Nonlinear Equations in Conformal Geometry - Part II

## Geometric PDE - Fully Nonlinear Equations in Conformal Geometry - Part I

## Geometric PDE - Fully Nonlinear Equations in Conformal Geometry

http://www.math.ias.edu/sp/gpde

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 the k-Yamabe problem, a fully nonlinear version of the Yamabe problem, and discuss the associated ellipticity condition and its geometric consequences.