  In this study we extend the concepts of $m$-pluripotential theory to the
Riemannian superspace formalism. Since in this setting positive supercurrents
and tropical varieties are closely related, we try to understand the relative
capacity notion with respect to the intersection of tropical hypersurfaces.
Moreover, we generalize the classical quasicontinuity result of Cartan to
$m$-subharmonic functions of Riemannian spaces and lastly we introduce the
indicators of $m$-subharmonic functions and give a geometric characterization
of their Newton numbers.
