Local geodesics for plurisubharmonic functions

We study geodesics for plurisubharmonic functions from the Cegrell class F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}_1$$\end{document} on a bounded hyperconvex domain of Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {C}}}^{n}$$\end{document} and show that, as in the case of metrics on Kähler compact manifolds, they linearize an energy functional. As a consequence, we get a uniqueness theorem for functions from F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}_1$$\end{document} in terms of total masses of certain mixed Monge–Ampère currents. Geodesics of relative extremal functions are considered and a reverse Brunn–Minkowski inequality is proved for capacities of multiplicative combinations of multi-circled compact sets. We also show that functions with strong singularities generally cannot be connected by (sub)geodesic arcs.