Deformation of anisotropic Fermi surfaces due to electron-electron   interactions
  We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface. 
Rafael Roldan, M. Pilar Lopez-Sancho, Francisco Guinea, and Shan-Wen   Tsai