关于Page和Chen-LeBrun-Weber度量的频谱
On the spectrum of the Page and the Chen-LeBrun-Weber metrics
摘要：
我们给出的第一个非零特征值的标量拉普拉斯的页和陈-LeBrun-韦伯爱因斯坦度量的界限。一个值得注意的特点是，这些边界获得没有明确的知识的度量或数值逼近。我们的方法还允许计算这两个度量的谱的不变部分。我们继续讨论这些界限的度量的线性稳定性的应用。我们还给出了数值证据表明，这两个度量的界限是非常接近的实际特征值。
英文摘要：
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 calculation 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
