My research is on elliptic partial differential equations of fully nonlinear type that appear in geometric problems, for instance, prescribed curvature. A classical problem of this type is the Minkowski problem which is strongly related to the Monge-Ampère equation. I am also interested in the geometry of hypersurfaces in both Riemannian and semi-Riemannian manifolds. This equations are usually represented as symmetric functions on the eigenvalues of the second fundamental form of the hypersurface with respect to the induced metric. Then we can study the properties of the prescription function to ensure the existence of such a hypersurface.