Recent progress on the Monge-Ampère equation

We consider convex solutions to the Monge-Ampere equation when the measure is doubling.We summarized the latest results on geometric and measure theoretic properties associatesto the solutions. We also discuss applications such as the real analysis related to the solutions and the Holder regularity of the gradient of the solutions.Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Maldonado, Diego. University of Kansas; Estados Unido