Timeline for Relationship between spectrum geometry and almost-isometry
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2011 at 7:19 | vote | accept | bobye | ||
| Mar 29, 2011 at 19:22 | answer | added | Otis Chodosh | timeline score: 2 | |
| Mar 29, 2011 at 11:55 | history | edited | bobye | CC BY-SA 2.5 |
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| Mar 29, 2011 at 11:44 | history | edited | bobye | CC BY-SA 2.5 |
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| Mar 29, 2011 at 11:42 | comment | added | bobye | Sorry, I failed to express my idea. My focus is about local structure, I misuse the concept of quasi-isometry. However I did not found a way to describe which two manifold are "almost" isometric. For example, the bounding surfaces of a non-rigid object may be "near" isometric of different poses. Their spectrum data seems be continuously change with respect to pose change. The deformation of a metric space will have corresponding change of their spectrum data. For two metric, considering their map $f$. inf{e: |d(x,y)-d(f(x),f(y)|< e} estimate compute min w.r.t $f$ | |
| Mar 29, 2011 at 11:38 | answer | added | ght | timeline score: 4 | |
| Mar 29, 2011 at 11:19 | comment | added | Paul Siegel | I don't think you're asking the right question: the theory of isospectral manifolds generally focuses on closed manifolds, but any two compact metric spaces are automatically quasi-isometric. Quasi-isometries don't care at all about local structure - they are best adapted to large scale problems involving non-smooth spaces. So it's hard to imagine what the sort of connection that you're asking about would look like. | |
| Mar 29, 2011 at 5:02 | history | asked | bobye | CC BY-SA 2.5 |