  We address at the mean field level the emergence of a Pomeranchuk instability
in a uniform Fermi liquid with \emph{central} particle-particle interactions.
We find that Pomeranchuk instabilities with all symmetries except $l=1$ can
take place if the interaction is repulsive and has a finite range $r_{0}$ of
the order of the inter-particle distance. We demonstrate this by solving the
mean field equations analytically for an explicit model interaction, as well as
numerical results for more realistic potentials. We find in addition to the
Pomeranchuk instability other, subtler phase transitions in which the Fermi
surface changes topology without rotational symmetry-breaking. We argue that
such interaction-driven topological transitions may be as generic to such
systems as the Pomeranchuk instability.
