  We introduce a new geometric characteristic of compact sets on the plane
called $r$-convexity, which fits nicely into the concept of generalized
convexity and extends essentially the conventional convexity. For a class of
subharmonic functions on unbounded domains with $r$-convex compact complement,
with the growth governed by the distance to the boundary, we obtain the
Blaschke--type condition for their Riesz measures. The result is applied to the
study of the convergence of the discrete spectrum for the Schatten--von Neumann
perturbations of bounded linear operators in the Hilbert space.
