Duke Mathematical Journal

Collapsing and the differential form Laplacian: The case of a smooth limit space

John Lott

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Abstract

We analyze the limit of the $p$-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the $p$-form Laplacian has small positive eigenvalues in a collapsing sequence.

Article information

Source
Duke Math. J., Volume 114, Number 2 (2002), 267-306.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1087575411

Digital Object Identifier
doi:10.1215/S0012-7094-02-11424-0

Mathematical Reviews number (MathSciNet)
MR1920190

Zentralblatt MATH identifier
1072.58023

Subjects
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 31C12: Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 35P15: Estimation of eigenvalues, upper and lower bounds

Citation

Lott, John. Collapsing and the differential form Laplacian: The case of a smooth limit space. Duke Math. J. 114 (2002), no. 2, 267--306. doi:10.1215/S0012-7094-02-11424-0. https://projecteuclid.org/euclid.dmj/1087575411


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