Timeline for A $n$-gon is isospectral to a regular $n$-gon (Isospectral $\implies$ isometry ?)
Current License: CC BY-SA 3.0
21 events
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| S Oct 27, 2016 at 0:22 | history | suggested | emiliocba |
The "isospectrality" tag is added.
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| Oct 27, 2016 at 0:10 | review | Suggested edits | |||
| S Oct 27, 2016 at 0:22 | |||||
| Jul 28, 2016 at 14:26 | history | edited | David Labrecque | CC BY-SA 3.0 |
deleted 1 character in body
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| Jul 28, 2016 at 3:47 | vote | accept | David Labrecque | ||
| Jul 28, 2016 at 3:00 | vote | accept | David Labrecque | ||
| Jul 28, 2016 at 3:47 | |||||
| Jul 28, 2016 at 2:31 | history | rollback | Yemon Choi |
Rollback to Revision 6
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| Jul 28, 2016 at 1:59 | vote | accept | David Labrecque | ||
| Jul 28, 2016 at 2:11 | |||||
| Jul 28, 2016 at 1:15 | answer | added | Neal | timeline score: 11 | |
| Jul 27, 2016 at 23:43 | history | edited | David Labrecque | CC BY-SA 3.0 |
edited title
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| Jul 27, 2016 at 23:07 | comment | added | Gerry Myerson | A websearch for "the sound of symmetry" came up with an EP by the metalcore band Sky Eats Airplane, but also with jstor.org/stable/10.4169/amer.math.monthly.122.9.815 (Lu and Rowlett, Amer Math Monthly 122 (November 2015) 815-835), which, I presume, is what OP had in mind. It might have been better for all, had OP told us what he knew when he first posted the question. | |
| Jul 27, 2016 at 20:13 | history | edited | Yemon Choi |
replaced Sharpie's tags with one that seems more appropriate
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| Jul 27, 2016 at 17:57 | comment | added | Neal | @NoamD.Elkies Yes, area and perimeter are (derivable from) coefficients in the heat trace. (One can also get a value derived from angles, see Mazzeo-Rowlette arxiv.org/abs/0901.0019) | |
| Jul 27, 2016 at 17:19 | history | edited | David Labrecque | CC BY-SA 3.0 |
deleted 1 character in body; edited title
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| Jul 27, 2016 at 16:30 | comment | added | Noam D. Elkies | Wasn't there a theorem that both area and perimeter are spectral invariants, whence $P \cong Q$ by the isoperimetric inequality? | |
| Jul 27, 2016 at 16:02 | history | edited | David Labrecque | CC BY-SA 3.0 |
edited title
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| Jul 27, 2016 at 14:10 | history | edited | David Labrecque | CC BY-SA 3.0 |
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| Jul 27, 2016 at 13:53 | comment | added | David Labrecque | @Neal Thanks for you answer. In fact, the problem isn't open since November 2015 (see Theorem 4, The Sound of Symmetry). I'm trying to prove that problem by myself in using something simpler; that why I wanted some clues. (P.S. Yes, I know the problem of Gordon-Webb-Wolpert. It is convenient to solve that problem before launching into a such problem.) | |
| Jul 27, 2016 at 13:34 | comment | added | Neal | Are you familiar with the examples from the 1990s (e.g. Gordon-Webb-Wolpert, Conway, others) constructed of isospectral planar polygons? If you wish to restrict to convex $n$_gons, I believe "isospectral $\Rightarrow$ isometric" is still open for convex domains in general. If $n=3$, it is known (Durso, Hillairet, Grieser-Maronna) that isospectral $\Rightarrow$ isometric. | |
| Jul 27, 2016 at 13:05 | history | edited | David Labrecque | CC BY-SA 3.0 |
added 11 characters in body
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| Jul 27, 2016 at 6:15 | review | First posts | |||
| Jul 27, 2016 at 6:40 | |||||
| Jul 27, 2016 at 6:11 | history | asked | David Labrecque | CC BY-SA 3.0 |