On the Space of m-subharmonic Functions

In this study, we investigate the space of m-subharmonic functions. We introduce the Mabuchi space of strictly m-subharmonic functions in an m-hyperconvex domain. We also study the metric properties of this space using Mabuchi geodesics. Some theoretical results are given in this study. We prove the connection between geodesics and homogeneous Hessian equations. The main result is important in the geometry of m-subharmonic functions. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.