Length and eigenvalue equivalence
| dc.creator | Leininger, Christopher J. | |
| dc.creator | McReynolds, D. B. | |
| dc.creator | Neumann, Walter D. | |
| dc.creator | Reid, Alan W. | |
| dc.date | 2006-06-14 | |
| dc.date | 2006-12-18 | |
| dc.date.accessioned | 2026-07-07T09:29:29Z | |
| dc.date.available | 2026-07-07T09:29:29Z | |
| dc.description | Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equivalent and primitive length equivalent Riemannian manifolds. For example we show that every finite volume hyperbolic $n$--manifold has pairs of eigenvalue equivalent finite covers of arbitrarily large volume ratio. We also show the analogous result for primitive length equivalence. | |
| dc.identifier | https://arxiv.org/abs/math/0606343 | |
| dc.identifier | http://arxiv.org/abs/math/0606343 | |
| dc.identifier | International Mathematics Research Notices 2007 (2007), rnm135-24 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157800 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.title | Length and eigenvalue equivalence | |
| dc.type | text |