We study geodesics for plurisubharmonic functions from the Cegrell class ${ \mathcal F}_1$ on a bounded hyperconvex domain of ${ \mathbb C}^n$ and show that, as in the case of metrics on K\"{ a}hler compact menifolds, they linearize an energy functional. As a consequence, we get a uniqueness theorem for functions from ${ \mathcal F}_1$ in terms of total masses of certain mixed Monge-Amp\`ere 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 arks.
Categories: math.CV