Timeline for A complete Riemannian metric for which the Ricci flow has no solution
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2014 at 2:09 | comment | added | Deane Yang | OK. I rewrote it. I hope it's OK. If not, please edit, replace, or suggest revisions. | |
| Jun 2, 2014 at 2:08 | history | edited | Deane Yang | CC BY-SA 3.0 |
Rewrote title and body.
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| Jun 2, 2014 at 1:10 | comment | added | S. Carnahan♦ | 3 of the votes came from the review process: mathoverflow.net/review/close/20382 The question could use a little help from someone with both domain knowledge and English skill. | |
| Jun 2, 2014 at 0:45 | comment | added | Igor Belegradek | Please do not close this. The question comes up naturally when one tries to pin down conditions under which the short time existence is true. As far as I know this is far from settled. | |
| Jun 1, 2014 at 23:11 | comment | added | Deane Yang | Why are there 4 votes to close this? | |
| Jun 1, 2014 at 14:59 | answer | added | Chih-Wei Chen | timeline score: 10 | |
| May 31, 2014 at 12:09 | comment | added | user9072 | I think the point of @Will Jagy's comment merely was to ask for context and motivation and/or to critique the use of an imperative. In any case it could help if intent of comments was made more clear. (There is some reason for the 15 character minimum.) | |
| May 29, 2014 at 6:13 | comment | added | Terry Tao | If you allow disconnected manifolds, this is easy, as one can just take the disjoint union of infinitely many spheres whose radii are going to zero (so each one blows up at a time that goes to zero also). Presumably one can join the spheres together by thin necks in order to obtain a connected example; or maybe one can take an infinitely long cylinder that is slowly tapering to zero. If the surface contains arbitrarily small minimal immersed spheres, then this paper of Colding-Minicozzi should do the trick: xxx.lanl.gov/abs/math.AP/0308090 . There may be an easier way though. | |
| May 29, 2014 at 4:38 | comment | added | Koma | Can you quote the paper of that kind of theorems? Thank you. @SanathDevalapurkar | |
| May 29, 2014 at 4:35 | review | Close votes | |||
| May 31, 2014 at 12:10 | |||||
| May 29, 2014 at 4:32 | comment | added | user62675 | @WillJagy There is a theorem stating that one can find a complete noncompact Riemannian manifold s/t the Ricci flowhas no solution, so I assume the OP is trying to find such an example. | |
| May 29, 2014 at 4:30 | comment | added | Koma | I don't know why. I read the paper "Ricci deformation of the metric on complete noncompact kahler manifolds" by Shi Wanxiong, and he said one can find this example. I am just interesting that the Ricci flow has no solution. What I know is that this example has unbound curvature since if it has bound curvature, Shi constructed a solution; and has no non-negative complex sectional curvature since the work of Wilking. @WillJagy | |
| May 29, 2014 at 2:42 | review | First posts | |||
| May 29, 2014 at 6:32 | |||||
| May 29, 2014 at 2:24 | history | asked | Koma | CC BY-SA 3.0 |