截断覆盖谱
The Cut-off Covering Spectrum
摘要：
引入了$R$截断覆盖谱和完备长度空间或黎曼流形的截断覆盖谱。光谱测量空间中局部空穴的大小，并使用称为$δ$覆盖和$R$截止$δ$覆盖的覆盖空间来定义。他们研究使用$δ$同伦，这是同伦通过网格的正方形被映射到球的半径$δ$。在局部紧空间上，我们证明了这些新的谱是长度谱闭包的子集。我们证明了$R$截止覆盖谱关于空间的点格罗莫夫-豪斯多夫收敛几乎连续，并且截止覆盖谱也是比较好的.这是不正确的覆盖谱定义在我们以前的工作，这是表现良好的紧空间。我们关闭分析这些频谱上的黎曼流形的截面和里奇曲率和他们的极限空间的下界。
英文摘要：
We introduce the $R$ cut-off covering spectrum and the cut-off covering spectrum of a complete length space or Riemannian manifold. The spectra measure the sizes of localized holes in the space and are defined using covering spaces called $δ$ covers and $R$ cut-off $δ$ covers. They are investigated using $δ$ homotopies which are homotopies via grids whose squares are mapped into balls of radius $δ$. On locally compact spaces, we prove that these new spectra are subsets of the closure of the length spectrum. We prove the $R$ cut-off covering spectrum is almost continuous with respect to the pointed Gromov-Hausdorff convergence of spaces and that the cut-off covering spectrum is also relatively well behaved. This is not true of the covering spectrum defined in our earlier work which was shown to be well behaved on compact spaces. We close by analyzing these spectra on Riemannian manifolds with lower bounds on their sectional and Ricci curvature and their limit spaces.
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。
