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2015 Partial collapsing and the spectrum of the Hodge–de Rham operator
Colette Anné, Junya Takahashi
Anal. PDE 8(5): 1025-1050 (2015). 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.

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Colette Anné. Junya Takahashi. "Partial collapsing and the spectrum of the Hodge–de Rham operator." Anal. PDE 8 (5) 1025 - 1050, 2015. https://doi.org/10.2140/apde.2015.8.1025

Information

Received: 13 June 2014; Accepted: 25 March 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1329.58024
MathSciNet: MR3393672
Digital Object Identifier: 10.2140/apde.2015.8.1025

Subjects:
Primary: 58J50
Secondary: 35P15 , 53C23 , 58J32

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

Rights: Copyright © 2015 Mathematical Sciences Publishers

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