论文标题
带有基本平均曲率纤维的Riemannian浸没的光谱估计值
Spectral estimates for Riemannian submersions with fibers of basic mean curvature
论文作者
论文摘要
对于带有基本平均曲率纤维的Riemannian浸没，我们将总空间的频谱与基本歧管上的Schrödinger操作员的光谱进行了比较。利用这一概念，我们研究了由谎言群体的行为引起的淹没。在这种情况下，我们将最先进的结果的状态扩展到Riemannian覆盖物下的频谱底部。作为应用程序，我们计算频谱的底部和连接的，可正常的谎言组的cheeger常数。
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.
