Timeline for Tangent cones at zero and infinity to minimal surfaces
Current License: CC BY-SA 4.0
6 events
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| Sep 6, 2022 at 18:18 | comment | added | SBK | OK sorry I didn't see the edit when I made the answer. But actually reading back I'm still confused. You ask about whether there is a pair that satisfies (1) strictly that isn't a blow-up/blow-down pair, but that would be asking literally whether there are two cones with different areas in the unit ball?? | |
| Sep 6, 2022 at 18:15 | history | undeleted | SBK | ||
| Sep 6, 2022 at 18:14 | history | deleted | SBK | via Vote | |
| Sep 6, 2022 at 17:49 | comment | added | Leo Moos | a singularity, does this constrain the blowdown cones you can get? (I mean, beyond the constraints for their densities that the monotonicity formula gives.) The first question is deliberately imprecise because I am interested in any answers: is there a topological or a variational relationship between the pair $(\mathbf{C}_0,\mathbf{C}_\infty)$? Can $\mathbf{C}_0$ have a 'bad' singular set if $\mathrm{sing} \, \mathbf{C}_\infty = \{0 \}$? Whether you work in the smoothly embedded class, or with area-minimizing currents or stationary varifolds, I'm interested in any information at all. | |
| Sep 6, 2022 at 17:45 | comment | added | Leo Moos | Thanks for the answer, but it's not quite what I was looking for. After your comments, I narrowed the question to consider only cones $\mathbf{C}_\infty$ with an isolated singularity, essentially to avoid examples such as the one you gave. As for the first question being open-ended, I disagree: it's a yes/no question. Now you could criticize that it's imprecise, but that's deliberate. What the question boils down to is this. If I have a blowdown cone $\mathbf{C}_\infty$, does this constrain what tangent cones I can get at singularities? What if I have the tangent cone $\mathbf{C}_0$ at [...] | |
| Sep 6, 2022 at 0:58 | history | answered | SBK | CC BY-SA 4.0 |