In this short note we prove a sector counting lemma for a class of Fermi surface on the plane which are $C^2$-differentiable and strictly convex. This result generalizes the one proved in \cite{ FKT} for the class of $C^{ 2+r}$-differentiable, $r\ge3$, strictly convex and strongly asymmetric Fermi surfaces, and the one proved in \cite{ FMRT} and \cite{ BGM1}, for the class of $C^2$-differentiable, strictly convex and central symmetric Fermi surfaces. This new sector counting lemma can be used to construct interacting many-fermion models for the doped graphene, in which the Fermi surface is extended and quasi-symmetric.
Categories: math-ph math.FA math.MG math.MP