  For a given finite subset $S$ of a compact Riemannian manifold $(M,g)$ whose
Schouten curvature tensor belongs to a given cone, we establish a necessary and
sufficient condition for the existence and uniqueness of a conformal metric on
$M \setminus S$ such that each point of $S$ corresponds to an asymptotically
flat end and that the Schouten tensor of the conformal metric belongs to the
boundary of the given cone. As a by-product, we define a purely local notion of
Ricci lower bounds for continuous metrics which are conformal to smooth metrics
and prove a corresponding volume comparison theorem.
