Timeline for Infinite number of closed geodesics on distorted sphere
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2022 at 13:22 | vote | accept | Joseph O'Rourke | ||
| Jan 17, 2022 at 12:56 | comment | added | Ali Taghavi | mathoverflow.net/questions/152513/… | |
| Jan 17, 2022 at 12:56 | comment | added | Ali Taghavi | @MoisheKohan In this regard please see this question too | |
| Jan 16, 2022 at 22:41 | comment | added | Moishe Kohan | @SamNead: Maybe I will post a question about the current status of the (notorious) conjecture on closed geodesics. The above reference claims a solution. By now the paper is 4 year old. Of course, especially during the pandemic, refereeing may take long time... | |
| Jan 16, 2022 at 13:01 | answer | added | Joseph O'Rourke | timeline score: 3 | |
| Jan 16, 2022 at 10:25 | comment | added | Sam Nead | @MoisheKohan - On page 27 we find "Theorem 6.14 (Main Result). Every closed Riemannian manifold M admits infinitely many geometrically distinct, non-constant, prime closed geodesics." There is no hypothesis on the dimension of M (to rule out the point and the circle). Trying to understand the first sentence of the proof (the definition of X given before 6.5) left me no wiser. | |
| Jan 16, 2022 at 2:50 | comment | added | Moishe Kohan | Incidentally, there is this paper claiming a proof of existence of infinitely many geometrically distinct closed geodesics on arbitrary closed Riemannian manifold of positive dimension. I do not know what's the status of the result. | |
| Jan 16, 2022 at 2:16 | comment | added | Will Jagy | good survey arxiv.org/pdf/1308.5417.pdf | |
| Jan 16, 2022 at 2:07 | comment | added | Will Jagy | Bangert, 1993, worldscientific.com/doi/abs/10.1142/… Refers to J. Franks, 1992, Inventiones | |
| Jan 16, 2022 at 1:36 | history | asked | Joseph O'Rourke | CC BY-SA 4.0 |