Comment on "Robustness of a Local Fermi Liquid against Ferromagnetism and Phase Separation"

In this paper we comment on the "Local Fermi Liquid Theory", proposed by Engelbrecht and Bedell [1]. We emphasize several important properties of the limit of infinite dimensions, in particular the k-dependence of the irreducible vertex function, the anisotropy of the Fermi surface and the necessary conditions for phase separation. It appears that these issues have not been fully appreciated in Ref. [1].