1206.5489 (Stuart James Hall et al.)

On the spectrum of the Page and the Chen-LeBrun-Weber metrics    [PDF]

Stuart James Hall, Thomas Murphy

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 requiring any explicit knowledge of the metric or numerical approximation to them. Our method also allows the calculation of 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 bound for both metrics are extremely close to the actual eigenvalue.

View original: http://arxiv.org/abs/1206.5489