Partial collapsing and the spectrum of the Hodge–de Rham operator

Anné, Colette; Takahashi, Junya

doi:10.2140/apde.2015.8.1025

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Partial collapsing and the spectrum of the Hodge–de Rham operator

Colette Anné and Junya Takahashi

Vol. 8 (2015), No. 5, 1025–1050

DOI: 10.2140/apde.2015.8.1025

Abstract

Our goal 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 by Mazzeo and Rowlett.

Keywords

Laplacian, Hodge–de Rham operator, differential form, eigenvalue, collapsing of Riemannian manifolds, conical singularity, elliptic boundary value problem

Mathematical Subject Classification 2010

Primary: 58J50

Secondary: 35P15, 53C23, 58J32

Milestones

Received: 13 June 2014

Accepted: 25 March 2015

Published: 28 July 2015

Authors

Colette Anné
Laboratoire de Mathématiques Jean Leray Université de Nantes CNRS, Faculté des Sciences BP 92208 44322 Nantes France

Junya Takahashi
Research Center for Pure and Applied Mathematics Tôhoku University Graduate School of Information Sciences 6-3-09 Aoba Sendai 980-8579 Japan

Vol. 8, No. 5, 2015