A Spectra comparison theorem and its applications
Abstract
We give a sharp comparison between the spectra of two Riemannian manifolds (Y,g) and (X,g0) under the following assumptions: (X,g0) has bounded geometry, (Y,g) admits a continuous Gromov-Hausdorff ε-approximation onto (X,g0) of non zero absolute degree, and the volume of (Y,g) is almost smaller than the volume of (X,g0). These assumption imply no restrictions on the local topology or geometry of (Y,g) in particular no curvature assumption is supposed or infered.
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