Vol. 8, No. 5, 2015

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Partial collapsing and the spectrum of the Hodge–de Rham operator

Colette Anné and Junya Takahashi

Vol. 8 (2015), No. 5, 1025–1050
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