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Research

The quaternionic Monge-Ampère equation and methods of pluripotential theory

Dongrui Wan (Shenzhen University)

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.