Timeline for Is displacement controled by stable norm?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2013 at 19:45 | comment | added | Benoît Kloeckner | @J. Martel: start from any metric, and along a small tubular neighborhood of a loop, change the metric to make it very small so that the loop becomes short (you can also make the metric very large in a thin layer around the loop so that it "disconnects" it from the rest of the manifold). | |
| Mar 7, 2013 at 18:15 | comment | added | JHM | I wish i knew what is the `tunnelling' phenomenon you are both referring to. | |
| Mar 6, 2013 at 18:11 | comment | added | Benoît Kloeckner | Moreover it seems to me that making a tunnel with a complicated shape forces you to make the metric very short inside it, possibly helping. | |
| Mar 6, 2013 at 18:09 | comment | added | Benoît Kloeckner | I know your example, but the additive constant here helps a lot: with $2\mathrm{diam}$ you have enough to enter the tunnel and go out of it. It follows that at least if you make the tunnel "linear" (everywhere roughly in the direction of your chosen primitive class, not wandering up and down), in such an example the upper bound I'd like to have does hold. | |
| Mar 6, 2013 at 14:51 | history | answered | Mikhail Katz | CC BY-SA 3.0 |