Dimensionality of Local Minimizers of the Interaction Energy
  In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin. 
D. Balagu\'e, J. A. Carrillo, T. Laurent and G. Raoul
math.AP