Timeline for Is every nonnegatively curved plane conformal to the complex plane?
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13 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2011 at 19:06 | comment | added | Mohan Ramachandran | Igor:Sorry for screwing up the references. | |
| Mar 16, 2011 at 20:43 | vote | accept | Igor Belegradek | ||
| Mar 16, 2011 at 20:09 | comment | added | Igor Belegradek | In Grigoryan's survey it is actually on page 177. ams.org/journals/bull/1999-36-02/S0273-0979-99-00776-4/… | |
| Mar 16, 2011 at 20:05 | answer | added | Mohan Ramachandran | timeline score: 7 | |
| Mar 16, 2011 at 20:01 | comment | added | Mohan Ramachandran | Igor:I realised after I made the comment that Milnor dealt with only the rotationally symmetric case. | |
| Mar 16, 2011 at 19:44 | comment | added | Igor Belegradek | Thanks, Mohan! I think I see how Cheng-Yau's result does the job, but I cannot figure out why Milnor's paper is relevant; where does he talk about volume, and does he really treat the non-rotationally symmetric case? Anyway, if you care to copy this comment into an answer, I would be happy to accept it. | |
| Mar 16, 2011 at 19:36 | comment | added | Mohan Ramachandran | Also see the paper of A Grigoryan Bulletin of AMS vol 36 pages 135 to 249 .Look at pages 172-173 . | |
| Mar 16, 2011 at 19:18 | comment | added | Mohan Ramachandran | Yes it implies parabolicity.In case of complete manifolds with non-negative ricci curvature and atmost quadratic volume growth parabolicity seems to have been prove by Cheng and Yau.In case of surfaces this is much older I believe you can find an argument in a paper of Milnor American Math Monthly vol 84 no 1 Jan 1977 pages 43-46 | |
| Mar 16, 2011 at 19:12 | comment | added | Igor Belegradek | Mohan, you are right that by Bishop-Gromov the volume growth is at most quadratic, and also at least linear (both things are true for complete open manifolds of nonnegative Ricci curvature). Does it imply parabolicity? I do not know much of these matters. | |
| Mar 16, 2011 at 18:56 | comment | added | Mohan Ramachandran | @Igor:Does'nt the volume grow at most like the euclidean plane by Bishop-Gromov or am I making a mistake?If the volume growth is atmost quadratic it is easy to show parabolicity. | |
| Oct 26, 2010 at 3:08 | vote | accept | Igor Belegradek | ||
| Mar 16, 2011 at 19:54 | |||||
| Oct 26, 2010 at 2:17 | answer | added | Anton Petrunin | timeline score: 12 | |
| Oct 26, 2010 at 1:58 | history | asked | Igor Belegradek | CC BY-SA 2.5 |