An inversion theorem in Fermi surface theory

We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between the fermions. This theorem gives a physical meaning to the counterterm function K that we use in the renormalization of these models: K can be identified as that part of the self--energy that causes the deformation of the Fermi surface when the interaction is turned on.