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

Hall, Stuart J. and Murphy, Thomas (2014) On the spectrum of the Page and the Chen-LeBrun-Weber metrics. Annals of Global Analysis and Geometry, 46 (1). pp. 87-101. ISSN 0232-704X


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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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10455-014-9412-6
Uncontrolled Keywords: Eigenvalues; Einstein metric
Subjects: Q Science > QA Mathematics
Divisions: School of Computing
Depositing User: Stuart Hall
Date Deposited: 07 Aug 2015 09:37
Last Modified: 07 Aug 2015 09:37
URI: http://bear.buckingham.ac.uk/id/eprint/49

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