Complete manifolds with bounded curvature and spectral gaps [article]

Richard Schoen, Hung Tran
2017 arXiv   pre-print
We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In particular, for any noncompact covering of a compact manifold, there is a metric on the base so that the lifted metric has an arbitrarily large finite number of gaps in its essential spectrum. Also, for any complete noncompact manifold with bounded curvature and
more » ... ve injectivity radius we construct a metric uniformly equivalent to the given one (also of bounded curvature and positive injectivity radius) with an arbitrarily large finite number of gaps in its essential spectrum.
arXiv:1510.05046v2 fatcat:dxahimnl75c67jx6wnm4rpyl3y