Timeline for A model of pillows
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jan 27, 2023 at 0:05 | history | bounty ended | CommunityBot | ||
| S Jan 27, 2023 at 0:05 | history | notice removed | CommunityBot | ||
| Jan 26, 2023 at 16:57 | comment | added | Fawen90 | Unless I miss something, do you mean the uniqueness of the maximizer (if it exists) is up to some constant? E.g. if $(u,v,w)$ is a maximizer, so it is with $(u+a,v+b,w)$ for any reals $a,b$. Can you please explain why this translation does not change your problem? | |
| Jan 24, 2023 at 21:35 | comment | added | Christophe Leuridan | What happens if $\Omega$ is a disk? Do you have an idea of the answer in this case? | |
| Jan 24, 2023 at 20:00 | comment | added | Daniel Castro | @MattF. This is for unit length edges. The corresponding sphere to compare would have radius 1/2 so the volume is $\pi/6\approx 0.5$, and we consider only half of it so the bound is $0.25$. | |
| Jan 24, 2023 at 14:21 | comment | added | user44143 | That number doesn’t seem right — a hemisphere with surface area $1$ has volume $(3\sqrt{2\pi})^{-1}\sim .133$, and isn’t that maximal for any volume with unit surface area? | |
| Jan 24, 2023 at 13:31 | comment | added | Daniel Castro | @M.Winter Thank you. Pak considers submetric mappings, meaning that the lengths of the geodesics are smaller than the lengths of their corresponding pre-images . Here we require that not the geodesics but some other curves (the ones aligned with the axes, that is, the warp and weft ) preserve their lengths. In that sense this mapping is less constrained. | |
| Jan 24, 2023 at 13:18 | comment | added | Daniel Castro | @MattF. $0.99\pm 0.02$. In the teabag problem it is $0.23/2$ (en.wikipedia.org/wiki/Paper_bag_problem) | |
| Jan 23, 2023 at 12:13 | comment | added | user44143 | What volume does your numerical simulation give? | |
| Jan 22, 2023 at 11:41 | comment | added | M. Winter | I don't know how related this is, but when I saw the pillow I was reminded of Igor Pak's article "Inflating Polyhedral Surfaces". | |
| Jan 19, 2023 at 14:11 | comment | added | PrimeRibeyeDeal | Is there a physical unit to measure squishiness or sponginess? That's something I've wondered and was reminded of by this question. | |
| S Jan 18, 2023 at 22:49 | history | bounty started | Daniel Castro | ||
| S Jan 18, 2023 at 22:49 | history | notice added | Daniel Castro | Draw attention | |
| Jan 17, 2023 at 23:08 | comment | added | Will Jagy | @LSpice here's a real one, based on observed behavior: a wedge of swans | |
| Jan 17, 2023 at 5:09 | comment | added | Ivan Izmestiev | Similar questions were studied in Paulsen, What is the shape of a mylar balloon?, Amer. Math. Monthly 101 (1994) and Pak, Schlenker, Profiles of inflated surfaces, Journal of Nonlinear Mathematical Physics, Volume 17, 2010 - Issue 2 | |
| Jan 16, 2023 at 23:52 | comment | added | LSpice | @WillJagy, an overflow of mathematicians? | |
| Jan 16, 2023 at 23:33 | comment | added | Will Jagy | I see. A pride of lions, a murder of crows, an exaltation of larks, a model of pillows. | |
| Jan 16, 2023 at 20:23 | history | asked | Daniel Castro | CC BY-SA 4.0 |