Title: Steady States of Rotating Stars and Galaxies,
Abstract: A rotating continuum of particles attracted to each other by gravity may be
modeled by the Euler-Poisson system. The existence of solutions is a very
classical problem. Here it is proven that a curve of solutions exists,
parametrized by the rotation speed, with a fixed mass independent of the speed.
The rotation is allowed to vary with the distance to the axis. A special case
is when the equation of state is $p=\rho^\gamma,\ 6/5<\gamma<2,\ \gamma\ne4/3$,
in contrast to previous variational methods which have required $4/3 < \gamma$.
The continuum of particles may alternatively be modeled microscopically by
the Vlasov-Poisson system. The kinetic density is a prescribed function. We
prove an analogous theorem asserting the existence of a curve of solutions with
constant mass. In this model the whole range $(6/5,2)$ is allowed, including
$\gamma=4/3$.