Timeline for Why is Fourier analysis so handy for proving the isoperimetric inequality?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 24, 2017 at 4:23 | comment | added | Willie Wong | @Turbo: the $x$ and $y$ coordinates along the curve are periodic functions if the curve is closed. | |
| Apr 30, 2017 at 8:11 | comment | added | Turbo | @DeaneYang 'a closed curve can be represented by a pair of periodic functions' is there an elementary example? | |
| Jun 8, 2010 at 14:49 | comment | added | Gil Kalai | I will also be very interested to learn a Fourier proof of the isoperimetric inequality for d>2.I was always very curious with the question why Fourier analysis is NOT handy forproving isoperimetric inequalities in dimension 3 and higher given the beautiful d=2 proof. | |
| Jun 6, 2010 at 1:35 | comment | added | Deane Yang | Arguably, the Brunn-Minkowski inequality is itself an isoperimetric inequality, so it's best to talk about how it is proved. Every proof I know involves some form of symmetrization via rearrangement (the fashionable terms is mass transportation). There are definitely deep connections between Brunn-Minkowski and Fourier analysis, but I will let people who understand this much better than me explain this. | |
| Jun 6, 2010 at 1:29 | comment | added | Victor Protsak | Just about the only way in higher dimensions is via Brunn-Minkowski inequality. Does it have any Fourier analytic meaning? | |
| Jun 5, 2010 at 23:09 | history | answered | Deane Yang | CC BY-SA 2.5 |