  We consider the equation $- \e^2 \D u + u= u^p$ in $\Omega \subseteq \R^N$,
where $\Omega$ is open, smooth and bounded, and we prove concentration of
solutions along $k$-dimensional minimal submanifolds of $\partial \O$, for $N
\geq 3$ and for $k \in \{1, ..., N-2\}$. We impose Neumann boundary conditions,
assuming $1<p <\frac{N-k+2}{N-k-2}$ and $\e \to 0^+$. This result settles in
full generality a phenomenon previously considered only in the particular case
$N = 3$ and $k = 1$.
