Timeline for Levy's isoperimetric inequality for sphere
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2017 at 14:54 | comment | added | Greg Kuperberg | Although it's been a long time, I think I learned it from Figiel, Lindenstrauss, Milman. I'm also not sure whether this proof is essentially different from the ones that you have seen. It may mainly be a matter of abbreviated vs detailed explanation. | |
| Mar 6, 2017 at 9:54 | vote | accept | Fedor Petrov | ||
| Mar 6, 2017 at 8:38 | comment | added | Jan Peter Schäfermeyer | Has this proof been published somewhere? I know two proofs that rely on Steiner symmetrization, one by Dinghas and one by Tippe whose descriptions sound considerably more complicated than the outline you have given. | |
| Oct 26, 2010 at 19:30 | comment | added | Greg Kuperberg | Convergence is based on the fact that the circumradius of $A$ can only go down under symmetrization. Moreover, if you do enough symmetrizations, it does go down unless $A$ is a spherical cap. | |
| Oct 26, 2010 at 13:32 | comment | added | Fedor Petrov | Ah, for $A'$ it depend only on one latitude (though maybe different from $H$), so here everything is OK. It remains to show that a sequence of symmetrizations converge to a hat, It should be standard. | |
| Oct 26, 2010 at 10:55 | comment | added | Greg Kuperberg | Yes, it's a proof by induction, even though $A_s \cap H$ depends on nearby latitudes. | |
| Oct 26, 2010 at 10:43 | comment | added | Fedor Petrov | ah, no, $A_s\cap H$ does not depend only on $A\cap H$, but on close lattitudes too... | |
| Oct 26, 2010 at 10:40 | comment | added | Fedor Petrov | $|A'_s\cap H|\leq A_s\cap H$ is induction propose if we use induction on dimension, right? | |
| Oct 26, 2010 at 10:32 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |