  We reconsider the virial theorem in the presence of a positive cosmological
constant Lambda. Assuming steady state, we derive an inequality of the form rho
>= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object.
With a minimum at Asphere = 2, its value can increase by several orders of
magnitude as the shape of the object deviates from a spherically symmetric one.
This, among others, indicates that flattened matter distributions like e.g.
clusters or superclusters, with low density, cannot be in gravitational
equilibrium.
