  The rich phenomenology of collective neutrino oscillations has been studied
only in one-dimensional or spherically symmetric systems. Motivated by the
non-spherical example of coalescing neutron stars, presumably the central
engines of short gamma-ray bursts, we use the Liouville equation to formulate
the problem for general source geometries. Assuming the neutrino ensemble
displays self-maintained coherence, the problem once more becomes effectively
one-dimensional along the streamlines of the overall neutrino flux. This
approach for the first time provides a formal definition of the ``single-angle
approximation'' frequently used for supernova neutrinos and allows for a
natural generalization to non-spherical geometries. We study the explicit
example of a disk-shaped source as a proxy for coalescing neutron stars.
