Subsolution theorem and the Dirichlet problem for the quaternionic Monge-Ampere equation

TL;DR

This paper proves the existence, stability, and subsolution theorems for quaternionic Monge-Ampère equations, solving the Dirichlet problem in strictly pseudoconvex domains within quaternionic space.

Contribution

It introduces new existence and stability results for quaternionic Monge-Ampère equations, extending classical theories to quaternionic settings.

Findings

Existence of solutions to the Dirichlet problem in quaternionic space.

Establishment of stability theorems for quaternionic Monge-Ampère equations.

Development of subsolution theorems in the quaternionic context.

Abstract

In this paper, the author studies quaternionic Monge-Amp\`ere equations and obtain the existence of the solutions to the Dirichlet problem for such equations in strictly pesudoconvex domains in quaternionic space. The stability and subsolution theorems are established for quaternionic Monge-Amp\`ere equations.