Timeline for Estimate on Covariant Derivatives of Coordinate Derivatives
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2019 at 14:06 | comment | added | Deane Yang | Finally, I would add that you're probably mostly interested in the Ricci flow for large time, so it's probably best to assume this result and move on. | |
| Feb 18, 2019 at 14:05 | comment | added | Deane Yang | Another approach that should work is the following: First, prove that if the curvature remains bounded on $[0,T)$, so do all of its covariant derivatives. Show that this implies the the flow extends smoothly to $[0,T$. This probably can be done by constructing time-dependent harmonic coordinates that depend smoothly on time. Now solve the Ricci flow on $[T,T+\epsilon)$. Show the extended solution is smooth across $t = T$. | |
| Feb 18, 2019 at 13:58 | comment | added | Deane Yang | I took a look at Topping's notes, and I don't quite understand the argument, either. But he's trying to prove a standard result, namely that if the curvature tensor remains bounded on a time interval $[0,T)$, then it can be extended to $[0,T+\epsilon)$ for some $\epsilon > 0$. This is a necessary basic first step in the study of the Ricci flow, so I'm sure there are other expositions of it, maybe in one of Ben Chow's books. | |
| Feb 17, 2019 at 19:01 | history | asked | Hollis Williams | CC BY-SA 4.0 |