Nonlinear partial Differential Equations

I intend to investigate two closely related classes of nonlinear partial differential equations: Hessian and curvature equations. These have a wide range of applications in differential geometry. Monge-Ampere equations are particularly important subclass having close connections to mass transfer problems, which have large range of applications in mathematics and in other fields. I will develop a comprehensive theory of these equations and their applications, encompassing boundary value problems, extremal solutions, mass transfer problems and curvature flow problems.