  We study the massive scalar field of a charged particle held at rest in
conical thin-shell spacetimes with one or two asymptotic regions. Resonant and
stable scalar Green's functions are characterized in terms of the coupling of
the field to the trace of the extrinsic curvature jump at the shell. Stable
coupling values, within the safety domain of the configuration parameters, are
used to analyze the self-force of static point charges.
