We prove a perturbative inversion theorem for the map between the interacti
ng and the noninteracting Fermi surface for a class of many fermion systems
with strictly convex Fermi surfaces and short-range interactions between t
he fermions, This theorem gives a physical meaning to the counterterm funct
ion K that we use in the renormalization of these models: K can be identifi
ed as that part of the self-enerey that causes the deformation of the Fermi
surface when the interaction is turned on. (C) 2000 John Wiley & Sons, Inc
.