The covering spectrum of a compact length space

Christina Sormani, Guofang Wei
2004 Journal of differential geometry  
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ > 0 which identify the distinct δ covers of the space. We investigate the relationship between this covering spectrum, the length spectrum, the marked length spectrum and the Laplace spectrum. We analyze the behavior of the covering spectrum under
more » ... ng spectrum under Gromov-Hausdorff convergence and study its gap phenomenon.
doi:10.4310/jdg/1099587729 fatcat:2ugdxnbdizf4vkbfrmjdvg4ywu