  Let M be a compact manifold equipped with a Riemannian metric g and a spin
structure \si. We let $\lambda (M,[g],\si)= \inf_{\tilde{g} \in [g]}
\lambda_1^+(\tilde{g}) Vol(M,\tilde{g})^{1/n}$ where $\lambda_1^+(\tilde{g})$
is the smallest positive eigenvalue of the Dirac operator D in the metric
$\tilde{g}$. A previous result stated that $\lambda(M,[g],\si) \leq
\lambda(\mS^n) =\frac{n}{2} \om_n^{{1/n}}$ where \om_n stands for the volume of
the standard n-sphere. In this paper, we study this problem for conformally
flat manifolds of dimension n \geq 2 such that D is invertible. E.g. we show
that strict inequality holds in dimension $n\equiv 0,1,2\mod 4$ if a certain
endomorphism does not vanish. Because of its tight relations to the ADM mass in
General Relativity, the endomorphism will be called mass endomorphism. We apply
the strict inequality to spin-conformal spectral theory and show that the
smallest positive Dirac eigenvalue attains its infimum inside the enlarged
volume-1-conformal class of g.
