  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.
