The spectrum of the Laplacian on forms.
The spectrum of the Laplacian on forms.
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拉普拉斯算子在形式上的谱。
DOI：
10.14288/1.0348220
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Zhiqin Lu
中科院分区：
文献类型：
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作者：
Nelia Charalambous;Zhiqin Lu
本文证明了Hilbert空间上自伴非负算子谱的Weyl判别法的一个推广。我们将应用这一新的准则结合Cheeger-Schuaya-Gromov和Cheeger-Colding理论来研究完备流形上的$k$-形式本质谱，其中完备流形在无穷远处的曲率为零或Ricci曲率渐近非负.
此外，我们将应用推广的Weyl准则来研究自伴算子在连续扰动下的谱的变化。在特殊情况下的拉普拉斯$k$-形式在一个完整的流形，我们将使用这些分析工具，以找到显着更强的结果，其频谱，包括其行为下的连续变形的度量的流形。
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory to study the $k$-form essential spectrum over a complete manifold with vanishing curvature at infinity or asymptotically nonnegative Ricci curvature.
In addition, we will apply the generalized Weyl criterion to study the variation of the spectrum of a self-adjoint operator under continuous perturbations of the operator. In the particular case of the Laplacian on $k$-forms over a complete manifold we will use these analytic tools to find significantly stronger results for its spectrum including its behavior under a continuous deformation of the metric of the manifold.