Timeline for Questions on smoothness of Riemann metrics
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 31, 2022 at 13:43 | history | edited | Anton Petrunin |
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| Apr 20, 2011 at 18:21 | comment | added | Igor Belegradek | A most recent discussion of these issues is the following paper [Taylor, Trans. Amer. Math. Soc. 358 (2006), 2415-2423] avaialble at ams.org/journals/tran/2006-358-06/S0002-9947-06-04090-6/… | |
| Apr 20, 2011 at 17:38 | comment | added | Andrew | @Deane Yang Thank you for DeTurck and Yang reference! I've read their later work, but didn'ty knew this one. Sorry, instead of global coordinates I should say a smooth atlas. | |
| Apr 20, 2011 at 17:34 | comment | added | Willie Wong | @Igor: you posted a link to the Georgia Tech proxy, which most of us cannot go through :-p. The link Igor meant to post is MR: ams.org/mathscinet-getitem?mr=MR2204038 article: dx.doi.org/10.1090/S0002-9947-06-04090-6 | |
| Apr 20, 2011 at 17:17 | vote | accept | Andrew | ||
| Apr 20, 2011 at 16:53 | history | edited | George Lowther | CC BY-SA 3.0 |
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| Apr 20, 2011 at 16:46 | comment | added | Willie Wong | On #2: if you believe that the best coordinates one can use is the harmonic ones, then in fact on any compact, closed manifold, you will not be able to extend the coordinates globally... | |
| Apr 20, 2011 at 16:21 | comment | added | Willie Wong | In fact, for #1, in the DeTurck-Kazdan paper you find a counterexample in the first paragraph. Note that in this case "changing coordinates" actually corresponds to changing atlas (as noted by Anton below). I wonder if for #1 you intend them to be Einstein manifolds? In which case the result is true using elliptic regularity. | |
| Apr 20, 2011 at 16:20 | answer | added | Deane Yang | timeline score: 7 | |
| Apr 20, 2011 at 16:18 | answer | added | Vladimir S Matveev | timeline score: 8 | |
| Apr 20, 2011 at 15:16 | answer | added | Anton Petrunin | timeline score: 14 | |
| Apr 20, 2011 at 14:07 | comment | added | Deane Yang | For #1, see: DeTurck, Dennis M.; Kazdan, Jerry L. Some regularity theorems in Riemannian geometry. Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 3, 249–260. You need assumptions on the curvature tensor (and its covariant derivatives) if you want higher regularity. I don't know what you mean by #2. Could you explain why the three-dimensional sphere has global co-ordinates? | |
| Apr 20, 2011 at 11:01 | history | asked | Andrew | CC BY-SA 3.0 |