Timeline for A non-Finsler metric on $\mathbb{R}^2$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 19, 2023 at 19:35 | vote | accept | Dmitrii Korshunov | ||
| Dec 17, 2023 at 23:00 | answer | added | Anton Petrunin | timeline score: 4 | |
| Dec 17, 2023 at 20:32 | comment | added | Dmitrii Korshunov | @AntonPetrunin very much interested! in this case i would like to have something which is not sub-Finsler too, and not of a cone-type singularity type suggested by YCor in the first comment. | |
| Dec 17, 2023 at 19:21 | comment | added | Anton Petrunin | Will you be interested in a 3-dimensional example? | |
| Mar 21, 2022 at 23:30 | history | edited | YCor |
edited tags
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| Nov 30, 2020 at 1:32 | comment | added | Moishe Kohan | See also 2nd answer here. | |
| Nov 29, 2020 at 23:33 | comment | added | Moishe Kohan | @YCor: Similar to Nikolaev's theorem characterizing Riemannian metrics among path metrics. The first condition would be local extendibility of geodesics, which fails in both examples that you gave. Compare my answers here and here. | |
| Nov 29, 2020 at 22:59 | comment | added | YCor | @MoisheKohan it's somewhat open-ended. Characterization in which terms? | |
| Nov 29, 2020 at 22:31 | comment | added | Moishe Kohan | The real question (originally due to Busemann) is "what is the characterization of Finsler distance functions among path-metrics on surfaces?" See "Foundations of singular Finsler geometry" by P.Andreev for some recent progress in this direction. | |
| Nov 29, 2020 at 19:25 | comment | added | YCor | What about the geodesic metric on the cone $x^2+y^2=z^2$, $z\ge 0$ (which is homeomorphic to the plane?) Or similarly, the quotient of $\mathbf{R}^2$ by $x\mapsto -x$, with distance induced by $\min(d(x,y),d(x,-y))$. | |
| Nov 29, 2020 at 19:23 | history | edited | YCor | CC BY-SA 4.0 |
fixed typos
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| Nov 29, 2020 at 19:09 | history | asked | Dmitrii Korshunov | CC BY-SA 4.0 |