  A large class of flat axially symmetric solutions to the Vlasov-Poisson
system is constructed with the property that the corresponding rotation curves
are approximately flat, slightly decreasing or slightly increasing. The
rotation curves are compared with measurements from real galaxies and
satisfactory agreement is obtained. These facts raise the question whether the
observed rotation curves for disk galaxies may be explained without introducing
dark matter. Furthermore, it is shown that for the ansatz we consider stars on
circular orbits do not exist in the neighborhood of the boundary of the steady
state.
