Timeline for (1-Lipschitz) + (length-preserving) = isometry
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 31, 2011 at 9:08 | comment | added | Anton Petrunin | Well for Lobachevsky plane the same works, but positive curvature of sphere makes some trouble, but it is not important. If the proof takes more than 10 lines then forget about it. | |
| Jul 30, 2011 at 0:26 | comment | added | Gjergji Zaimi | When I have some free time, I will try to work out the details, but I do believe that such an elementary solution is possible. As for the sphere, I thought that assuming the polygonal edges are great circle arcs, one can go through with similar calculations. | |
| Jul 29, 2011 at 22:43 | comment | added | Anton Petrunin | Right, polygonal is easy. In fact the inequality for the angles follows immediately. But even for polygonal one has to work a bit for the case of sphere. On the other hand I see some technical difficulties in your approximation. It seems that the way indicated in the post scriptum is easier to write (but still unpleasant). | |
| Jul 29, 2011 at 17:47 | history | answered | Gjergji Zaimi | CC BY-SA 3.0 |