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Spectral Estimates for Riemannian Submersions with Fibers of Basic Mean Curvature
The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2021-03-22 , DOI: 10.1007/s12220-021-00634-z
Panagiotis Polymerakis

For Riemannian submersions with fibers of basic mean curvature, we compare the spectrum of the total space with the spectrum of a Schrödinger operator on the base manifold. Exploiting this concept, we study submersions arising from actions of Lie groups. In this context, we extend the state-of-the-art results on the bottom of the spectrum under Riemannian coverings. As an application, we compute the bottom of the spectrum and the Cheeger constant of connected, amenable Lie groups.



中文翻译:

基本平均曲率光纤的黎曼浸没光谱估计

对于具有基本平均曲率的纤维的黎曼浸没式,我们将总空间的光谱与基本流形上的Schrödinger算子的光谱进行比较。利用这个概念,我们研究了由李群的行动引起的沉没。在这种情况下,我们将最新结果扩展到黎曼覆盖下的光谱底部。作为应用,我们计算频谱的底部和连接的,可满足的李群的Cheeger常数。

更新日期:2021-03-22
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