Dipartimento di Scienze di Base e Applicate per l'Ingegneria

It is well known that every isolated singularity of a graph of constant mean curvature must be removable. However, this is not longer true for other graphs as those of constant Gauss curvature. We use a geometric approach for classifying the isolated singularities of the Hessian one equation and the constant positive Gaussian curvature graphs. Using this point of view for these geometric PDEs, we classify the isolated singularities of the general Monge-Ampère equation.