We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.
- Collapsing of Riemannian manifolds
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology