  We study Bose-Einstein condensates with purely dipolar interactions in oblate
(pancake) traps. We find that the condensate always becomes unstable to
collapse when the number of particles is sufficiently large. We analyze the
instability, and find that it is the trapped-gas analogue of the
``roton-maxon'' instability previously reported for a gas that is unconfined in
two dimensions. In addition, we find that under certain circumstances, the
condensate wave function attains a biconcave shape, with its maximum density
away from the center of the gas. These biconcave condensates become unstable
due to azimuthl excitation - an angular roton.
