Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem

We consider the equation -epsilon(2) Delta u + u = u(p) in Omega subset of R-N, where Omega is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of partial derivative ohm, for N >= 3 and for k is an element of {1, . . . , N - 2}. We impose Neumann boundary conditions, assuming 1 < p < ( N - k + 2)/(N - k - 2) and is an element of -> 0(+). This result settles in full generality a phenomenon previously considered only in the particular case N = 3 and k = 1.