Timeline for Analytic dependence on the metric
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2013 at 8:57 | vote | accept | Klaus Kröncke | ||
| Jun 5, 2013 at 7:06 | answer | added | Rafe Mazzeo | timeline score: 3 | |
| Jun 4, 2013 at 18:13 | comment | added | Otis Chodosh | @Deane Yang, I've added an explanation. | |
| Jun 4, 2013 at 17:42 | answer | added | Otis Chodosh | timeline score: 4 | |
| May 27, 2013 at 7:40 | comment | added | Klaus Kröncke | This is not discussed in Besse's book. I had a look before. It is not explicitly mentioned in the Paper by Sun and Wang (on the Kähler-Ricci flow near a Kähler-Einstein metric) but I think analytic means that the map $g\mapsto scal_g$ is analytic between the Banach spaces C^{k,\alpha}\to C^{k-2,\alpha}$ if it is $C^{\infty}$ Gateaux differentiable and around each metric, there is a neighborhood where the power series converges to the functional. | |
| May 24, 2013 at 19:59 | comment | added | Deane Yang | I'm curious about this. Probably I don't know what "analytic" means in this context. Could one of you explain how "analytic" is used in this setting? | |
| May 24, 2013 at 18:10 | comment | added | Otis Chodosh | Why do you want a reference if you've just given the proof? I imagine that this sort of things are discussed in Besse "Einstein Manifolds",(because I think that fact is used) but I couldn't find with a brief glance. | |
| May 24, 2013 at 16:14 | history | asked | Klaus Kröncke | CC BY-SA 3.0 |