Timeline for Classes for which the Spectrum determines a Convex Shape
Current License: CC BY-SA 3.0
13 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| May 21, 2016 at 8:47 | comment | added | Hu xiyu | well,i am thinking the same problem and i think we don't own all the tool to deal with this,for example,we know in dimension 4 ,there is two weyl shambles convex,isospectral but not isometry,what is the difference between dim 2 and dim 4? | |
| S Feb 24, 2016 at 14:41 | history | suggested | emiliocba |
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| Feb 24, 2016 at 14:28 | review | Suggested edits | |||
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| Dec 23, 2013 at 22:02 | comment | added | Beni Bogosel | @OtisChodosh: I was doing some numerical computations yesterday on exactly the same thing (Faber-Krahn for polygons), obtaining regular polygons, as expected. | |
| Dec 23, 2013 at 21:33 | comment | added | Otis Chodosh | The following paper contains some information about it (and some related questions): projecteuclid.org/… | |
| Dec 23, 2013 at 21:32 | comment | added | Otis Chodosh | Nice question by the way! Here's a related open problem which I think is quite nice (sort of related to your "almost isospectral" question for $k=1$): What is the Faber-Krahn (en.wikipedia.org/wiki/…) inequality on polygons? In other words, what $n$-gon of fixed area minimizes the first Dirichlet eigenfunction? For $n=3,4$ (triangles, quadrilaterals) it is known that the minimizer is the regular $n$-gon. Polya and Szego conjectured that this holds for $n\geq 5$ but very little progress has been made! | |
| Dec 23, 2013 at 21:19 | history | edited | Beni Bogosel | CC BY-SA 3.0 |
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| Dec 22, 2013 at 19:52 | comment | added | Beni Bogosel | @OtisChodosh: Thanks. I have found a few interesting articles. | |
| Dec 22, 2013 at 18:56 | comment | added | Otis Chodosh | Google 'hearing the shape of a triangle' for a proof that a triangle is determined by its spectrum | |
| Dec 22, 2013 at 17:46 | history | edited | Beni Bogosel | CC BY-SA 3.0 |
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| Dec 21, 2013 at 1:00 | history | edited | Beni Bogosel |
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| Dec 21, 2013 at 0:55 | history | asked | Beni Bogosel | CC BY-SA 3.0 |