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

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 estimat...

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Vydané v:	Annals of global analysis and geometry Ročník 46; číslo 1; s. 87 - 101
Hlavní autori:	Hall, Stuart J., Murphy, Thomas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.06.2014 Springer Nature B.V
Predmet:	Analysis Approximation Differential Geometry Eigenvalues Explicit knowledge Geometry Global Analysis and Analysis on Manifolds Laplace transforms Mathematical models Mathematical Physics Mathematics Mathematics and Statistics Studies Theorems Toric-Kähler metric Ricci flow Einstein metric Linear stability Spectrum of Laplacian
ISSN:	0232-704X, 1572-9060
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Popis
Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0232-704X 1572-9060
DOI:	10.1007/s10455-014-9412-6