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Partial collapsing and
the spectrum of the Hodge–de Rham operator
Colette Anné and Junya Takahashi |
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Vol. 8 (2015), No. 5, 1025–1050
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 58J50
Secondary: 35P15, 53C23, 58J32
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Milestones
Received: 13 June 2014
Accepted: 25 March 2015
Published: 28 July 2015
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Authors |
| Colette Anné | |
| Laboratoire de Mathématiques Jean
Leray Université de Nantes CNRS, Faculté des Sciences BP 92208 44322 Nantes France |
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| Junya Takahashi | |
| Research Center for Pure and Applied
Mathematics Tôhoku University Graduate School of Information Sciences 6-3-09 Aoba Sendai 980-8579 Japan |
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