  We explore the structure and dynamics of dipolar Bose-Einstein condensates
(DBECs) near their threshold for instability. Near this threshold a DBEC may
exhibit nontrivial, biconcave density distributions, which are associated with
instability against collapse into "angular roton" modes. Here we discuss
experimental signatures of these novel features. In the first, we infer local
collapse of the DBEC from the experimental stability diagram. In the second, we
explore the dynamics of collapse and find that a nontrivial angular
distribution is a signature of the DBEC possessing a biconcave structure.
