Timeline for Gap between first two nonzero Laplacian eigenvalues on closed compact surface?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 2, 2013 at 19:15 | comment | added | Ian Agol | There can be no universal lower bound, since the multiplicity of $\lambda_1$ can vary over moduli space, and thus there are surfaces with the difference arbitrarily close to $0$. That is why in my answer I interpret your question as asking for an upper bound, which I show exists for hyperbolic surfaces. The reason to restrict to the hyperbolic case is that one cannot probably not say much for general Riemannian metrics on surfaces. | |
| May 2, 2013 at 18:26 | answer | added | Ian Agol | timeline score: 3 | |
| May 2, 2013 at 13:34 | comment | added | TerronaBell | @Rbega: both. Or any kind of (reasonably precise) estimate, really. | |
| May 2, 2013 at 13:32 | comment | added | TerronaBell | @Kofi: I say nonzero because I don't care about the zero eigenvalue corresponding to the constant function. | |
| May 2, 2013 at 13:29 | comment | added | TerronaBell | @Algol: without multiplicity. Otherwise you are very right that the answer is not very interesting. :-) | |
| May 2, 2013 at 13:27 | history | edited | TerronaBell | CC BY-SA 3.0 |
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| May 2, 2013 at 11:40 | answer | added | Marc Palm | timeline score: 1 | |
| May 2, 2013 at 10:21 | comment | added | Rbega | Are you interested in upper bounds, lower bounds or both? | |
| May 2, 2013 at 9:15 | comment | added | Matthias Ludewig | Probably one should skip the "nonzero" requirement as in this case, the gap is always positive. | |
| May 2, 2013 at 5:27 | comment | added | Ian Agol | The smallest non-zero eigenvalue can have multiplicity $>1$, so in this case is the gap zero? Or are you counting without multiplicity? | |
| May 2, 2013 at 5:05 | history | asked | TerronaBell | CC BY-SA 3.0 |