Timeline for Exponential convergence of Ricci flow
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2023 at 12:22 | history | edited | Gabe K | CC BY-SA 4.0 |
Fixing a very small typo in the normalized solution
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| Apr 28, 2021 at 17:04 | vote | accept | Gabe K | ||
| Apr 28, 2021 at 0:01 | answer | added | RBega2 | timeline score: 4 | |
| Apr 27, 2021 at 18:37 | comment | added | YangMills | Small update to my first comment: it actually converges smoothly and exponentially fast to some (potentially different) KE metric. | |
| Apr 27, 2021 at 18:11 | comment | added | YangMills | Of course, it is also known that when a KE metric exists then the volume-normalized flow (starting at any Kahler metric in the anticanonical cohomology class) does converge to some KE, see e.g. arxiv.org/pdf/1207.5441.pdf | |
| Apr 27, 2021 at 18:10 | comment | added | YangMills | For a more recent take on these issues in the case of the (volume normalized) Kahler-Ricci flow on Fano manifolds which admit KE metrics, in all complex dimensions (so including $S^2$) see arxiv.org/pdf/0705.4048.pdf, in particular Remark (7) at the very end of the paper: they show that if the flow converges to a KE metric smoothly modulo automorphisms(=gauge change), then it actually converges smoothly and exponentially fast (without the need for any gauge change). | |
| Apr 27, 2021 at 17:28 | answer | added | Otis Chodosh | timeline score: 5 | |
| Apr 26, 2021 at 19:32 | comment | added | RBega2 | I believe there are issues with the gauge that are creeping in. I glanced at Hamilton's paper and it seems he proves exponential convergence of a modified flow (where there is a term that I think is supposed to correspond to the soliton potential in the limit. Of course there is no non-trivial soliton on the the two sphere so you then can recover the desired exponential convergence. | |
| Apr 26, 2021 at 18:03 | history | edited | Gabe K | CC BY-SA 4.0 |
I added a shorter version of the question so that the post is more readable.
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| Apr 26, 2021 at 4:03 | history | asked | Gabe K | CC BY-SA 4.0 |