Hodge-Laplace Operator on Compact Manifolds from Which a Finite Number of Balls Is Omitted

We study here the convergence of eigenvalues and eigenforms of the Laplace operator Δ = (dδ + δd) acting on differential forms in the perturbation obtained by omitting a finite number of little balls on a compact Riemannian manifold M. We restrict ourselves to absolute boundary conditions by duality and show the convergence except at degree (dim(M) − 1) where new harmonic forms and one small eigenvalue appear on the perturbed manifold.