Based on the fact that the Neumann Green function can be constructed as a
perturbation of the fundamental solution by a single-layer potential, we
establish gaussian two-sided bounds for the Neumann Green function for a
general parabolic operator. We build our analysis on classical tools coming
from the construction of a fundamental solution of a general parabolic operator
by means of the so-called parametrix method. At the same time we provide a
simple proof for the gaussian two-sided bounds for the fundamental solution. We
also indicate how our method can be adapted to get a gaussian lower bound for
the Neumann heat kernel of a compact Riemannian manifold with boundary having
non negative Ricci curvature