Partial collapsing and the spectrum of the Hodge Laplacian

Colette Anné (1) , Junya Takahashi (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Division of Mathematics

The goal of the present paper is to calculate the limit spectrum of the Hodge-de Rham operator under the perturbation of collapsing one part of a manifold obtained by gluing together two manifolds with the same boundary. It appears to take place in the general problem of blowing up conical singularities as introduced in \cite{Maz} and \cite{Row1,Row2}.

Mots clés: Laplacian; Hodge-de Rham operator; differential forms; eigenvalues; collapsing of Riemannian manifolds; Atiyah-Patodi-Singer type boundary condition

Domaines: Géométrie différentielle [math.DG]

Colette Anné, Junya Takahashi. Partial collapsing and the spectrum of the Hodge Laplacian. 2010. ⟨hal-00503230v3⟩