  We consider the Hele-Shaw flow that arises from injection of two-dimensional
fluid into a point of a curved surface. The resulting fluid domains have and
are more or less determined implicitly by a mean value property for harmonic
functions. We improve on the results of Hedenmalm and Shimorin \cite{HS} and
obtain essentially the same conclusions while imposing a weaker curvature
condition on the surface. Incidentally, the curvature condition is the same as
the one that appears in a recent paper of Hedenmalm and Perdomo, where the
problem of finding smooth area minimizing surfaces for a given curvature form
under a natural normalizing condition was considered. Probably there are deep
reasons behind this coincidence.
