  A general theory of partial balayage on Riemannian manifolds is developed,
with emphasis on compact manifolds. Partial balayage is an operation of
sweeping measures, or charge distributions, to a prescribed density, and it is
closely related to (construction of) quadrature domains for subharmonic
functions, growth processes such as Laplacian growth and to weighted
equilibrium distributions.
  Several examples are given in the paper, as well as some specific results.
For instance, it is proved that, in two dimensions, harmonic and geodesic balls
are the same if and only if the Gaussian curvature of the manifold is constant.
