  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.
