  Suppose that $\Sigma=\partial M$ is the $n$-dimensional boundary of a
connected compact Riemannian spin manifold $( M,\langle\;,\;\rangle)$ with
non-negative scalar curvature, and that the (inward) mean curvature $H$ of
$\Sigma$ is positive. We show that the first eigenvalue of the Dirac operator
of the boundary corresponding to the conformal metric
$\langle\;,\;\rangle_H=H^2\langle\;,\;\rangle$ is at least $n/2$ and equality
holds if and only if there exists a parallel spinor field on $ M$. As a
consequence, if $\Sigma$ admits an isometric and isospin immersion $\phi$ with
mean curvature $H_0$ as a hypersurface into another spin Riemannian manifold $
M_0$ admitting a parallel spinor field, then \begin{equation} \label{HoloIneq}
\int_\Sigma H\,d\Sigma\le \int_\Sigma \frac{H^2_0}{H}\, d\Sigma \end{equation}
and equality holds if and only if both immersions have the same shape operator.
In this case, $\Sigma$ has to be also connected. In the special case where
$M_0=\R^{n+1}$, equality in (\ref{HoloIneq}) implies that $M$ is an Euclidean
domain and $\phi$ is congruent to the embedding of $\Sigma$ in $M$ as its
boundary. We also prove that Inequality (\ref{HoloIneq}) implies the Positive
Mass Theorem (PMT). Note that, using the PMT and the additional assumption that
$\phi$ is a strictly convex embedding into the Euclidean space, Shi and Tam
\cite{ST1} proved the integral inequality \begin{equation}\label{shi-tam-Ineq}
\int_\Sigma H\,d\Sigma\le \int_\Sigma H_0\, d\Sigma, \end{equation} which is
stronger than (\ref{HoloIneq}) .
