Timeline for Nash embedding theorem for 2D manifolds
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2011 at 18:40 | comment | added | j.c. | My above comment was written too carelessly; see mathoverflow.net/questions/78026/… for more detailed discussion. | |
| Oct 12, 2010 at 1:13 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Dean -> Deane !
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| Sep 8, 2010 at 15:38 | comment | added | j.c. | If you allow immersions, then Poznyak proved that $\mathbb{R}^4$ works for any compact part of a complete surface. In particular, regarding Anton's comment above, this implies that surfaces admit local embeddings into $\mathbb{R}^4$. Compactness is important for Gromov's result - apparently it's not known whether the hyperbolic plane has a smooth isometric embedding in $\mathbb{R}^5$, though Blanusa constructed one in $\mathbb{R}^6$. The book by Han and Hong cited by BS in his answer is a good source for many of these questions. | |
| Sep 7, 2010 at 21:18 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Precise Gromov reference added.
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| Sep 7, 2010 at 1:46 | vote | accept | CommunityBot | ||
| Sep 4, 2010 at 23:00 | comment | added | Willie Wong | I think Gromov's result may be in his Partial Differential Relations book (I am not sure: I am travelling right now and don't have it with me). | |
| Sep 4, 2010 at 13:56 | vote | accept | CommunityBot | ||
| Sep 7, 2010 at 1:46 | |||||
| Sep 4, 2010 at 13:56 | vote | accept | CommunityBot | ||
| Sep 4, 2010 at 13:56 | |||||
| Sep 4, 2010 at 13:16 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
Revised to make clear that it is the embedding which is C^1 or C^2
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| Sep 4, 2010 at 12:47 | history | answered | Joseph O'Rourke | CC BY-SA 2.5 |