  We provide a detailed proof of the fact that any domain which is sufficiently
flat in the sense of Reifenberg is also Jones-flat, and hence it is an
extension domain. We discuss various applications of this property, in
particular we obtain L^\infty estimates for the eigenfunctions of the Laplace
operator with Neumann boundary conditions. We also compare different ways of
measuring the "distance" between two sufficiently close Reifenberg-flat
domains. These results are pivotal to the quantitative stability analysis of
the spectrum of the Neumann Laplacian performed in another paper by the same
authors.
