The quaternionic Monge-Ampere equation and methods of pluripotential theory

Abstract: In this talk, we will discuss some potential results for the quaternionic Monge-Ampère equations. We generalize the pluripotential theory for the complex Monge-Ampère operator to that for the quaternionic Monge-Ampère operator, and develop the theory of quaternionic closed positive currents on quaternionic space. By using these results, we study the continuity and stability of quaternionic Monge-Ampère equations. Moreover, we will discuss several results about the Dirichlet problem of quaternionic Monge-Ampère equations.