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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Vydáno v:Annals of global analysis and geometry Ročník 46; číslo 1; s. 87 - 101
Hlavní autoři: Hall, Stuart J., Murphy, Thomas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.06.2014
Springer Nature B.V
Témata:
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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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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-014-9412-6