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On the spectrum of the Page and the Chen-LeBrun-Weber metrics

par Hall, Stuart James;Murphy, Thomas
Référence Annals of global analysis and geometry, 46, 1, page (87-101)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

We give bounds on the first non-zero eigenvalue of the scalar Laplacian for both the Page and the Chen-LeBrun-Weber Einstein metrics. One notable feature is that these bounds are obtained without explicit knowledge of the metrics or numerical approximation to them. Our method also allows the estimation of the invariant part of the spectrum for both metrics. We go on to discuss an application of these bounds to the linear stability of the metrics. We also give numerical evidence to suggest that the bounds for both metrics are extremely close to the actual eigenvalue. © 2014 Springer Science+Business Media Dordrecht.