P-spectrum and collapsing of connected sums, calculus of the limit

Colette Anné (1) , Junya Takahashi (2)

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

The goal of the paper is to calculate the limit sectrum of the Hodge-Laplace operator under the perturbation of collapse of one part of a connected sum. This gives some new results concerning the 'conformal spectrum' on differential forms.

Mots clés: Hodge-Laplacian; Dirac type operator; engenvalues; collapsing of Riemannian manifolds

Domaines: Géométrie différentielle [math.DG]

Colette Anné, Junya Takahashi. P-spectrum and collapsing of connected sums, calculus of the limit. Transactions of the American Mathematical Society, 2012, 364 (4), pp.1711-1735. ⟨hal-00293459v3⟩