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$ p$-spectrum and collapsing of connected sums


Authors: Colette Anné and Junya Takahashi
Journal: Trans. Amer. Math. Soc. 364 (2012), 1711-1735
MSC (2010): Primary 58J50; Secondary 35P15, 53C23, 58J32
DOI: https://doi.org/10.1090/S0002-9947-2011-05351-1
Published electronically: November 10, 2011
MathSciNet review: 2869189
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Abstract | References | Similar Articles | Additional Information

Abstract: The goal of the present paper is to calculate the limit of the spectrum of the Hodge-de Rham operator under the perturbation of collapse of one part of a connected sum. It takes place in the general problem of blowing up conical singularities introduced by R. Mazzeo and J. Rowlett.


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Additional Information

Colette Anné
Affiliation: Laboratoire de Mathématiques Jean Leray, CNRS-Université de Nantes, Faculté des Sciences, BP 92208, 44322 Nantes, France
Email: colette.anne@univ-nantes.fr

Junya Takahashi
Affiliation: Division of Mathematics, Graduate School of Information Sciences, Tôhoku University, Aoba 6-3-09, Sendai, 980-8579, Japan
Email: t-junya@math.is.tohoku.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2011-05351-1
Keywords: Laplacian, Hodge-de Rham operator, differential forms, eigenvalue, collapsing of Riemannian manifolds, Atiyah-Patodi-Singer type boundary condition.
Received by editor(s): July 21, 2009
Received by editor(s) in revised form: March 8, 2010
Published electronically: November 10, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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