Timeline for Small energy implies a lifting $\rho e^{i\theta}$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2019 at 14:15 | comment | added | fedja | Only on a big set. On a small set $|u|$ can be as far from $1$ as you want. | |
| Jun 2, 2019 at 14:10 | comment | added | R. N. Marley | But always, independently of the dimension, $|u|$ is close to $1$ if the energy is small, isnt it? The problem is that $\theta $ is not $H^1(T^N)$ when $N>1$. Am I right? | |
| Jun 1, 2019 at 22:29 | comment | added | fedja | Only in dimension $1$. In higher dimensions you can create a function with arbitrarily small energy that vanishes on an open set, after which you can change it a bit on that open set to make the argument $\theta$ behaving in a bad way. | |
| Jun 1, 2019 at 17:20 | history | asked | R. N. Marley | CC BY-SA 4.0 |