Zero and negative eigenvalues of the conformal Laplacian

Rod Gover; Asma Hassannezhad; Dmitry Jakobson; Michael Levitin

doi:10.4171/JST/142

Zero and negative eigenvalues of the conformal Laplacian

Rod Gover, Asma Hassannezhad, Dmitry Jakobson, Michael Levitin

School of Mathematics

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Abstract

We show that zero is not an eigenvalue of the conformal Laplacian for generic Riemannian metrics. We also discuss non-compactness for sequences of metrics with growing number of negative eigenvalues of the conformal Laplacian.

Original language	English
Pages (from-to)	793-806
Number of pages	14
Journal	Journal of Spectral Theory
Volume	6
Issue number	4
Early online date	9 Dec 2016
DOIs	https://doi.org/10.4171/JST/142
Publication status	Published - 2016

Keywords

Spectral geometry
conformal geometry
conformal Laplacian
eigenvalue 0
negative eigenvalues
generic metrics
manifolds of metrics
pre-compactness

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title = "Zero and negative eigenvalues of the conformal Laplacian",

abstract = "We show that zero is not an eigenvalue of the conformal Laplacian for generic Riemannian metrics. We also discuss non-compactness for sequences of metrics with growing number of negative eigenvalues of the conformal Laplacian.",

keywords = "Spectral geometry, conformal geometry, conformal Laplacian, eigenvalue 0, negative eigenvalues, generic metrics, manifolds of metrics, pre-compactness",

author = "Rod Gover and Asma Hassannezhad and Dmitry Jakobson and Michael Levitin",

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journal = "Journal of Spectral Theory",

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publisher = "European Mathematical Society",

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T1 - Zero and negative eigenvalues of the conformal Laplacian

AU - Gover, Rod

AU - Hassannezhad, Asma

AU - Jakobson, Dmitry

AU - Levitin, Michael

PY - 2016

Y1 - 2016

N2 - We show that zero is not an eigenvalue of the conformal Laplacian for generic Riemannian metrics. We also discuss non-compactness for sequences of metrics with growing number of negative eigenvalues of the conformal Laplacian.

AB - We show that zero is not an eigenvalue of the conformal Laplacian for generic Riemannian metrics. We also discuss non-compactness for sequences of metrics with growing number of negative eigenvalues of the conformal Laplacian.

KW - Spectral geometry

KW - conformal geometry

KW - conformal Laplacian

KW - eigenvalue 0

KW - negative eigenvalues

KW - generic metrics

KW - manifolds of metrics

KW - pre-compactness

U2 - 10.4171/JST/142

DO - 10.4171/JST/142

M3 - Article (Academic Journal)

SN - 1664-039X

VL - 6

SP - 793

EP - 806

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 4

ER -

Zero and negative eigenvalues of the conformal Laplacian

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Keywords

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