Construction of solutions for a nonlinear elliptic problem on Riemannian   manifolds with boundary
  Let (M,g) be a smooth compact, n dimensional Riemannian manifold,with smooth n-1 dimensional boundary. We prove that the stable critical points of the mean curvature of the boundary generates solutions for a singularly perturbed elliptic problem with Neumann boundary conditions . 
Marco G. Ghimenti, Anna Maria Micheletti
math.AP