Timeline for Geodesics in $\mathbb{R}^2 \times \mathbb{S}^1$ under "segment" metric
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 11 at 14:27 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Sep 24, 2011 at 14:07 | comment | added | Jean-Marc Schlenker | Thanks Joseph. Actually I'm not sure it's that useful, because the Wasserstein metric geodesics will not respect the structure of the segments -- you'll have segments at the beginning and at the end, but not in between. In other terms the space of segments is a kind of submanifold in the space of measures, but it's not geodesic. Back to your original question, it's probably necessary to do a computation to obtain the ODE describing geodesics, as mentioned by Sergei. | |
| Sep 23, 2011 at 16:12 | comment | added | Joseph O'Rourke | I just found that the book, Gradient flows: in metric spaces and in the space of probability measures, contains a chapter entitled, "The Wasserstein distance and its behavior along geodesics." This may help. | |
| Sep 23, 2011 at 16:04 | comment | added | Joseph O'Rourke | Thanks, J.-M.! I would never have looked at this, although I have heard of its alias, the earth mover's distance. Great connection! | |
| Sep 23, 2011 at 15:43 | history | answered | Jean-Marc Schlenker | CC BY-SA 3.0 |