Timeline for Is it overkill to invoke Kirszbraun theorem to prove the following fact ?
Current License: CC BY-SA 3.0
4 events
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| Mar 1, 2012 at 18:45 | comment | added | Anton Petrunin | @Thomas: No, it does not work. The map which you are suggesting is called line-of-sight map; look at the Example on page 71 in our book. math.psu.edu/petrunin/papers/alexandrov-geometry/the-book.pdf | |
| Mar 1, 2012 at 8:39 | comment | added | Thomas Richard | I let it go for the moment, but if I found a construction I'll let you know. The reason I thought it may be possible is that I think, correct me if I'm wrong, it is possible to 1-Lipschitz fill a triangle in a $CAT(0)$ space by its comparison triangle in the plane using a explicit construction. I think choosing a vertex $a$ of the triangle and parametrize $[bc]$ by a constant speed curve $\gamma(t)$ for $t\in[0,1]$, then let $\sigma_t(s)$ be the constant speed geodesic from $a$ to $\gamma$, and associate $(t,s)$ to $\sigma_t(s)$ both in the $CAT(0)$ and the model space does the job. | |
| Feb 29, 2012 at 23:58 | comment | added | Anton Petrunin | I would be surprised if it is an overkill, but I like surprises. | |
| Feb 29, 2012 at 13:25 | history | asked | Thomas Richard | CC BY-SA 3.0 |