Timeline for Does the length spectrum determine the volume?
Current License: CC BY-SA 3.0
6 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Mar 29, 2022 at 1:59 | comment | added | David Roberts♦ | The link in Ian's comment is broken, here's a replacement: arxiv.org/abs/math/0407422 | |
| Mar 1, 2012 at 23:40 | comment | added | Ian Agol | For Euclidean manifolds, the Laplace spectrum does not determine the length spectrum. front.math.ucdavis.edu/0407.5422 | |
| Mar 1, 2012 at 18:50 | comment | added | BS. | I knew about hyperbolic surfaces, but somehow forgot to mention that this was known, and indeed since 1959, which I find quite remarkable. But the Zoll case is new to me. Thanks. | |
| Mar 1, 2012 at 17:15 | comment | added | alvarezpaiva | Thanks BS. In the reference you give (the preprint by Kelmer) it is stated that Huber proved that for hyperbolic surfaces the length spectrum and the spectrum of the Laplacian determine each other (Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959) 1–26). Therefore, it is true that the length spectrum of a compact hyperbolic surface determines its volume. Another case where this happens is Zoll manifolds. This was known as the weak Blaschke conjecture and was settled by Yang and Reznikov. | |
| Mar 1, 2012 at 15:18 | history | answered | BS. | CC BY-SA 3.0 |