Timeline for Largest hyperbolic disk embeddable in Euclidean 3-space?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2023 at 23:02 | review | Low quality posts | |||
| Nov 5, 2023 at 7:18 | |||||
| Jan 5, 2023 at 2:34 | comment | added | Akiva Weinberger | @NoahSnyder I meant the Springer link in j.c.'s comment ("Yeah, I was just looking at the journal version of that article…"). But I guess the other one broke as well | |
| Jan 5, 2023 at 2:17 | comment | added | Noah Snyder | @AkivaWeinberger: Thanks, fixed! | |
| Jan 5, 2023 at 2:16 | history | edited | Noah Snyder | CC BY-SA 4.0 |
Updated dead link
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| Jan 4, 2023 at 21:03 | comment | added | Akiva Weinberger | @j.c. Link is broken | |
| Oct 15, 2009 at 1:28 | comment | added | j.c. | I guess that they're saying that there are corners where the ruffles start to form. | |
| Oct 15, 2009 at 1:23 | comment | added | j.c. | There's some more discussion in the text below figure 12 in that paper: "Note that, when you crotchet beyond the annular strip that lies flat and forms a complete annulus, the surface begins to form ruffles and is no longer a surface of revolution. In fact, it appears that it is not even differentiable where the ruffles start, for the "top ridge" of the ruffles (see Figure 12) appears to be straight and thus not tangent to the plane of the complete annulus." | |
| Oct 15, 2009 at 1:20 | comment | added | j.c. | Yeah, I was just looking at the journal version of that article to see if there were more details, and there the sentence reads "The finite surfaces described here can apparently be extended indefinitely, but they appear always not to be differentiably embedded (see Figure 12)." Figure 12 is a picture of one of their crotcheted surfaces with the center pulled up so that it kind of looks like a pseudosphere, with the caption "Crotcheted pseudosphere". | |
| Oct 15, 2009 at 1:14 | comment | added | Noah Snyder | I'm confused, my reading of that link is that they don't give a C^1 embedding of the whole hyperbolic plane. But I can't see how they wouldn't be C^1 for arbitrarily large (but finite) radius. | |
| Oct 15, 2009 at 0:56 | comment | added | j.c. | That's actually the reason I put in C^2 in my question. There's a recent book on isometric embeddings, by Han and Hong, which tackles related problems from an analysis viewpoint. There seem to be plenty of results on local isometric embedding without any explicit bounds or constructions, unless there are general ways to back out bounds from such proofs that I'm not aware of. | |
| Oct 15, 2009 at 0:50 | comment | added | S. Carnahan♦ | I should point out that the crochet article linked above has references to research literature. In particular, it mentions that there are no C^2 embeddings of the whole plane, but there is a C^1 embedding. | |
| Oct 15, 2009 at 0:47 | comment | added | j.c. | It's my reading of the second link that these crotcheted surfaces are not even C^1 though. Thanks for the links though. | |
| Oct 15, 2009 at 0:38 | history | answered | Noah Snyder | CC BY-SA 2.5 |