The Hessian equation in quaternionic space

Abstract

In this paper, we introduce $m$-subharmonic functions in quaternionic space ${\mathbb{H}}^n$, we define the quaternionic Hessian operator and solve the homogeneous Dirichlet problem for the quaternionic Hessian equation on the unit ball with continuous boundary data.

arXiv admin note: text overlap with arXiv:1901.07080 by other authors