Timeline for The Isoperimetric problem for domains constrained to lie between two parallel planes
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2020 at 21:41 | vote | accept | Jules | ||
| May 12, 2013 at 21:24 | comment | added | Will Jagy | Oh, including contact pieces with the planes. That explains the oval pictures. | |
| May 12, 2013 at 20:47 | comment | added | Rbega | I see your point. I think you're right that the correct boundary condition is that the surface meet the planes tangentially and so the Delanauy has least area. | |
| May 12, 2013 at 20:25 | history | edited | Rbega | CC BY-SA 3.0 |
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| May 12, 2013 at 19:32 | comment | added | Douglas Zare | I think the nodoid I mentioned, a Delauney surface, is better than the piece of the sphere. If you have two surfaces meeting at a non-straight angle along a curve, then I think you can locally decrease the area without changing the volumes of the complementary regions. Note that Jules looked at $\sqrt{a^2-x^2}+b$ not $\sqrt{(a+b)^2 - x^2}$. The former makes straight angles with the circular cap, but does not have constant mean curvature when $b \gt 0$. | |
| May 12, 2013 at 18:10 | history | answered | Rbega | CC BY-SA 3.0 |