A REMARK ON THE PERTURBATION OF CRITICAL MANIFOLDS

Given a C~2-function f on a Hilbedrt Riemannian manifold M, let ∑ be a. nondegonerate critical manifold of f, what becomes of ∑, if we perturbe f to f+g? When g is a C~2 perturbation, i.e. ||g||c~2 is small, there was a result due to M. Reeken by the inverse function theorem. It was rediscovered by Ambrosetti et.