Timeline for First eigenvalue of the Laplacian on a regular polygon
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2023 at 16:26 | answer | added | Beni Bogosel | timeline score: 2 | |
| Mar 2, 2016 at 19:56 | comment | added | BigM | @WillieWong The case $n=3,4$ was proven by Polya. See, for instance Henrot's paper. As far as I understand, for $n\geq 5$, Steiner symmetrization method increases the number of sides. | |
| Jun 24, 2015 at 9:23 | answer | added | user122986 | timeline score: 4 | |
| Jun 13, 2015 at 17:51 | comment | added | Otis Chodosh | This is well known to be open. I think that the $N=3,4$ cases can be found in Polya and Szego's book "Isoperimetric Inequalities in Mathematical Physics." But the proof is not hard if you know that Steiner symmetrization decreases the first eigenvalue. | |
| Jun 11, 2015 at 12:33 | answer | added | Beni Bogosel | timeline score: 8 | |
| Jun 4, 2015 at 8:07 | comment | added | Magi | I edited the question :) | |
| Jun 4, 2015 at 8:06 | history | edited | Magi | CC BY-SA 3.0 |
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| Jun 4, 2015 at 7:47 | comment | added | Willie Wong | Can you include, in your question, the literature for N = 3,4? | |
| Jun 4, 2015 at 7:27 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
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| Jun 4, 2015 at 7:07 | review | First posts | |||
| Jun 4, 2015 at 7:27 | |||||
| Jun 4, 2015 at 7:03 | history | asked | Magi | CC BY-SA 3.0 |