hal-00503230, version 1

Partial collapsing and the spectrum of the Hodge Laplacian

Colette Anné () ¹, Junya Takahashi () ²

(2010-07-17)

• 1:  Laboratoire de Mathématiques Jean Leray (LMJL)
• http://www.math.sciences.univ-nantes.fr/jeanleray/
  CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes France
• 2:  Division of Mathematics
• 
  Ministère de l'Enseignement Supérieur et de la Recherche Scientifique Graduate School of Information Sciences Tôhoku University, Aoba 09, Sendai, 980-8579 Japan

Available versions :  v1 (2010-07-17) v2 (2011-02-21) v3 (2011-09-02) v4 (2012-04-10)

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject: Mathematics/Differential Geometry
• Title: Partial collapsing and the spectrum of the Hodge Laplacian
• Abstract: The goal of the present paper 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 in \cite{Maz} and \cite{Row1,Row2}.
• Fulltext language: English
• Production date: 2010-07-17
• Keyword(s): Laplacian – Hodge-de Rham operator – differential forms – eigenvalues – collapsing of Riemannian manifolds – Atiyah-Patodi-Singer type boundary condition
• Classification: MSC 58J50; Secondary 35P15, 53C23, 58J32
• Comment: 23 pages

Attached file list to this document: 

• hal-00503230, version 1
• http://hal.archives-ouvertes.fr/hal-00503230
• oai:hal.archives-ouvertes.fr:hal-00503230
• From: Colette Anné <>
• Submitted on: Saturday, 17 July 2010 13:35:57
• Updated on: Saturday, 17 July 2010 20:56:35