We give a sharp comparison between the spectra of two Riemannian manifolds (Y, g) and (Formula presented.) under the following assumptions: (Formula presented.) has bounded geometry, (Y, g) admits a continuous Gromov–Hausdorff (Formula presented.) -approximation onto (Formula presented.) of non zero absolute degree, and the volume of (Y, g) is almost smaller than the volume of (Formula presented.). These assumptions imply no restrictions on the local topology or geometry of (Y, g) in particular no curvature assumption is supposed or inferred.
A spectra comparison theorem and its applications / Cerocchi, Filippo. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 282:3-4(2016), pp. 715-730. [10.1007/s00209-015-1561-1]
A spectra comparison theorem and its applications
Cerocchi, Filippo
2016
Abstract
We give a sharp comparison between the spectra of two Riemannian manifolds (Y, g) and (Formula presented.) under the following assumptions: (Formula presented.) has bounded geometry, (Y, g) admits a continuous Gromov–Hausdorff (Formula presented.) -approximation onto (Formula presented.) of non zero absolute degree, and the volume of (Y, g) is almost smaller than the volume of (Formula presented.). These assumptions imply no restrictions on the local topology or geometry of (Y, g) in particular no curvature assumption is supposed or inferred.| File | Dimensione | Formato | |
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