  By means of mean-field theory, we have studied the structure and excitation
spectrum of a purely dipolar Bose gas in pancake-shaped trap where the
confinement in the x-y plane is provided by a highly anharmonic potential
resulting in an almost uniform confinement in the plane. We show that the
stable condensates is characterized by marked radially structured density
profiles. The stability diagram is calculated by independently varying the
strength of the interaction and the trap geometry. By computing the Bogoliubov
excitation spectrum near the instability line we show that soft "angular"
rotons are responsible for the collapse of the system. The free expansion of
the cloud after the trap is released is also studied by means of time-dependent
calculations, showing that a prolate, cigar-shaped condensate is dynamically
stabilized during the expansion, which would otherwise collapse. Dipolar
condensates rotating with sufficiently high angular velocity show the formation
of multiply-quantized giant vortices, while the condensates acquire a
ring-shaped form.
