Timeline for Applications of cut locus structure theorems
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2017 at 11:29 | vote | accept | Andrew Whelan | ||
| May 25, 2017 at 11:51 | comment | added | coudy | Milnor's article is actually one page long. ncbi.nlm.nih.gov/pmc/articles/PMC300113/pdf/pnas00178-0006.pdf I also like the explicit constructions of non-isometric isospectral surfaces in the book of P. Buser, "Geometry and spectra of compact Riemann surfaces" ch12 . This is quite visual, just by gluing pair of pants. Finally I just noticed that the drum problem has its own wikipedia page en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum. This may be a starting point. | |
| May 25, 2017 at 10:44 | comment | added | Andrew Whelan | Hi coudy, thanks for your answer - I'm intrigued by the potential link to harmonic analysis (+1)! However, I'm skeptical about how exhibiting two isometrically distinct tori would appeal to applied mathematicians unless I could show they are isospectral. Could you perhaps spell this out a little more or provide a link to the basic theory which could help me figure this out? It would appear to me (www-fourier.ujf-grenoble.fr/~pberard/D/isos-dea93.pdf) that the tori are isospectral only if the squared lengths of the vertices on the dual lattices are the same, but I may have misunderstood | |
| May 24, 2017 at 20:28 | history | edited | coudy | CC BY-SA 3.0 |
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| May 24, 2017 at 20:21 | history | answered | coudy | CC BY-SA 3.0 |