Theory of fermion condensation as an analog of the liquid-drop theory of   atomic nuclei
  Employing the duality between the momentum distribution $n(p)$ and density distribution $\rho(r)$, problems of theory of systems with flat bands, pinned to the Fermi surface, are discussed. We propose that the Lifshitz topological phase transition associated with the formation of additional pockets of the Fermi surface is the precursor of fermion condensation. 
V.A. Khodel
cond-mat.str-el