Journal of Spectral Theory


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Volume 6, Issue 4, 2016, pp. 793–806
DOI: 10.4171/JST/142

Published online: 2016-12-09

Zero and negative eigenvalues of the conformal Laplacian

A. Rod Gover[1], Asma Hassannezhad[2], Dmitry Jakobson[3] and Michael Levitin[4]

(1) University of Auckland, New Zealand
(2) Bonn, Germany
(3) McGill University, Montreal, Canada
(4) University of Reading, UK

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

Gover A. Rod, Hassannezhad Asma, Jakobson Dmitry, Levitin Michael: Zero and negative eigenvalues of the conformal Laplacian. J. Spectr. Theory 6 (2016), 793-806. doi: 10.4171/JST/142