Timeline for Is the structure constant additive on connected components?
Current License: CC BY-SA 3.0
8 events
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| May 30, 2014 at 13:01 | comment | added | Giovanni De Gaetano | I'm sorry for the annoyance, and for taking back the acceptance of the answer. But reviewing my computations I found out that I didn't get your point. In the sense that the fact that the Laplacian scales with a factor $\gamma^{-\chi/3}$ is clear, as well as the examples in the article you linked. What is not clear is how this would ensure additivity of the structural constant on connected components instead of spoiling it. Are you sure of this fact? Thanks for your willingness! | |
| May 22, 2014 at 13:40 | comment | added | Giovanni De Gaetano | Thank you very much! Now it's clear, I was under the unfortunate misconception that the spectral zeta function in $0$ had value $1$! | |
| May 22, 2014 at 13:39 | vote | accept | Giovanni De Gaetano | ||
| May 30, 2014 at 13:01 | |||||
| May 21, 2014 at 12:53 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| May 21, 2014 at 12:52 | comment | added | Carlo Beenakker | added some elaboration, hope this is helpful | |
| May 21, 2014 at 12:47 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| May 21, 2014 at 7:54 | comment | added | Giovanni De Gaetano | Thanks for your answer Carlo! On one hand I see that $c_{\Delta, \mu}(M) = \log(\mathrm{det}^*(\Delta_{\mu\,\mathrm{vol}(M)^{-1},M}))$, but on the other hand I do not see the rescaling factor you claim for the determinant of Laplacians once you scale the metric. I could be missing something extremely trivial, but just computing it I get: $\mu'= \gamma^2\,\mu$ implies $\Delta_{\mu'} = \gamma^{-2} \Delta_\mu$ which implies $\log(\mathrm{det}^*(\Delta_{\mu'} = \log(\mathrm{det}^*(\Delta_\mu))- \log(\gamma^2)$. Could I please ask you to elaborate a bit more? | |
| May 19, 2014 at 13:19 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |