Timeline for the left hand side of the Ricci flow equation at the initial value
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 18, 2023 at 14:50 | comment | added | The Amplitwist |
The links to springerlink.com are broken. I'm also unable to find any snapshots saved on the Wayback Machine.
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| Nov 24, 2013 at 16:32 | comment | added | Otis Chodosh | @BenoîtKloeckner Sorry, perhaps my wording is a bit incorrect: I only meant that someone might (as I first did when reading the comment) think that it was supposed to require that the flow could be "backed up" slightly. | |
| Nov 24, 2013 at 16:28 | comment | added | Deane Yang | I'm pretty sure there are different gauges (metric-dependent choice of local co-ordinates) that work. For eaxmple, my guess is that defining a time-dependent co-ordinates that are harmonic at time $t$ with respect to $g(t)$ would work. As for using co-ordinates that are harmonic at time $t = 0$ but not necessarily for $t > 0$, I think this should work as well. The error term will be second order but small, so in integral estimates, one should be able to control them using the Laplacian term (and integration by parts). | |
| Nov 24, 2013 at 9:08 | comment | added | Benoît Kloeckner | But we can interpret this kind of equations at $t=0$, don't we? One can either use Misha's definition of smoothness (smoothly extendable to a neighborhood of $0$) while remembering that we do not ask the equation to be satisfied for negative times; or define differentiable functions on closed intervals in the natural way (Taylor formula to order $1$). | |
| Feb 19, 2013 at 16:46 | history | edited | Otis Chodosh | CC BY-SA 3.0 |
minor changes
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| May 9, 2012 at 1:08 | comment | added | Otis Chodosh | @timur, I'm no expert, but those are the only two methods I know. Harmonic coordinates might be useful? See Chow-Knopf p 91, where they sort of discuss this, without making any precise claims. It's not clear to me, however, that they work, as I dont know how "far from harmonic" at time $t>0$ coordinates are which are harmonic at $t=0$. | |
| May 8, 2012 at 22:23 | comment | added | timur | @Otis, can I ask a quick naive question: Is there any other approach to local existence results except Hamilton's original approach and the one using the DeTurck method? In particular, why harmonic coordinates cannot be used? | |
| May 8, 2012 at 20:05 | comment | added | Otis Chodosh | No problem! I assume that Terry Tao has something to say about this at his blog, which you might find helpful. | |
| May 8, 2012 at 20:01 | comment | added | kassandra | Otis, thanks particularly for your valuable references to the literature. | |
| May 8, 2012 at 19:58 | vote | accept | kassandra | ||
| May 8, 2012 at 19:16 | history | answered | Otis Chodosh | CC BY-SA 3.0 |