Timeline for Ricci curvature under rough convergence
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2014 at 17:51 | comment | added | Anton Petrunin | @ChrisGerig, I do not see ambiguity in the question. In fact it takes some effort to formulate the collapsing version of the statement without optimal transport (try to do this). | |
| Mar 24, 2014 at 14:08 | comment | added | Otis Chodosh | @ChrisGerig, thanks for your comment! I was thinking of "easy case" when I asked the question, but am interested in general! | |
| Mar 24, 2014 at 7:05 | comment | added | Chris Gerig | @AntonPetrunin, I spoke to John Lott, who remarked that there is an ambiguity in what the OP is after. The easy case is where the manifolds are of the same dimension. But his proof can handle the case where the limiting manifold has a different dimension (and for which he is unaware of an alternative proof). | |
| Mar 24, 2014 at 2:41 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Mar 23, 2014 at 22:21 | vote | accept | Otis Chodosh | ||
| Mar 23, 2014 at 22:21 | comment | added | Otis Chodosh | Thanks! This is excellent. I believe jstor.org/stable/2951841 is the paper you mean. | |
| Mar 23, 2014 at 19:31 | comment | added | Anton Petrunin | P.S. also, it should be known that if $m$-dimensional manifolds with lower bound for Ricci curvature GH-converge to an $m$-dimensional manifold then it converges in measured Gromov--Hausdorff sense. It is Colding's result if I remember right, likely he also proved the statement you asked. | |
| Mar 23, 2014 at 19:22 | history | answered | Anton Petrunin | CC BY-SA 3.0 |