Timeline for Tangent cones at zero and infinity to minimal surfaces
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Sep 25 at 6:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 28 at 5:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 29 at 5:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 1, 2023 at 4:09 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 14, 2023 at 5:50 | comment | added | H_Wang | I guess the simplest example is two different Lawson's cones $(C^{p, q}, C^{p', q'})$, here $p'<p\leq q<q'$, $p+q = p'+q'\geq 8$. Note that two Lawson's cones have the same density at origin iff they are equivalent by an ambient isometry. On the other hand, [Simon-Solomon '86] proved that any stationary integral varifold asymptotic to a multiplicity one Lawson's cone $C$ near infinity is translation of either $C$ itself or the Hardt-Simon foliation on one-side of $C$, thus, the only blow-up-blow-down pair with $C_\infty$ to be a Lawson's cone must have $C_0$ planar. | |
| Jun 3, 2023 at 3:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 3, 2023 at 2:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 6, 2022 at 1:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 6, 2022 at 20:16 | comment | added | Otis Chodosh | I would imagine that something might be true, but at the moment we know basically nothing. (For starters, we don't even have that many examples of stable cones, particularly ones without lots of symmetry, although there are probably tons). | |
| Sep 6, 2022 at 3:06 | comment | added | Leo Moos | @OtisChodosh I'll take a look at Nick's stuff, thanks for the pointer! Would you expect the blow-up at the singularity to be related with $\mathbf{C}_\infty$? Say some constraints via topology, or the Morse index of their links? | |
| Sep 6, 2022 at 2:57 | comment | added | Otis Chodosh | I think it's a an open problem to find M with an isolated singularity but no boundary (other than a cone). One expects this to occur as blowups of intermediate scales in degenerating min surf in R8 for example. See the work of Edelen. | |
| Sep 6, 2022 at 0:58 | answer | added | SBK | timeline score: 0 | |
| Sep 5, 2022 at 23:29 | history | edited | LSpice | CC BY-SA 4.0 |
`\operatorname` and `\label`+`\eqref`
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| Sep 5, 2022 at 23:16 | history | edited | Leo Moos | CC BY-SA 4.0 |
narrowed scope to clarify question
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| Sep 5, 2022 at 22:33 | history | edited | Leo Moos | CC BY-SA 4.0 |
added examples to clarify question
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| Sep 5, 2022 at 17:31 | history | edited | Leo Moos | CC BY-SA 4.0 |
little omission
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| Sep 5, 2022 at 17:29 | comment | added | Leo Moos | Yeah, you're right - I should have commented on equality in the monotonicity inequality. I'll fix it in a second. | |
| Sep 5, 2022 at 17:22 | comment | added | RBega2 | An obvious example is two multiplicity one hyperplanes that are not parallel. Actually, this works for any pair of cones with the same density which are not equal. | |
| Sep 5, 2022 at 17:18 | history | asked | Leo Moos | CC BY-SA 4.0 |