一个Kröger型谱不等式的反例
Counter-example to a Kröger type spectral inequality
摘要：
给定一个黎曼流形，外尔定律表明拉普拉斯算子的谱如何渐近。由于这一结果，人们越来越有兴趣寻找与这一定律相容的几何边界。在超曲面的情况下，等周比是一个自然的几何量，它允许从上面限制频谱。我们调查的问题，并找到一个例子的超曲面的特征值由等周比minorated。
英文摘要：
Given a Riemannian manifold, Weyl's law indicates how the spectrum of the Laplacian behaves asymptotically. Because of that result, there has been a growing interest in finding geometrical bounds compatible with this law. In the case of hypersurfaces, the isoperimetric ratio is a natural geometrical quantity, that allows to bound the spectrum from above. We investigate the problem and find an example of hypersurface where the eigenvalues are minorated by the isoperimetric ratio.
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