Timeline for Does there exist energy-minimizing immersions?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2018 at 22:26 | comment | added | Piotr Hajlasz | @DeaneYang There is an explicit example due to Iwaniec and Onninen of not attaining minimum in my answer. | |
| Mar 26, 2018 at 15:07 | answer | added | Piotr Hajlasz | timeline score: 5 | |
| Mar 26, 2018 at 14:22 | comment | added | Deane Yang | This is the scale invariant energy, so you would not expect a minimum to always exist. A bubble can form, where a fixed part (the bubble), often with nontrivial topology, of the domain maps into a point. In particular, this was studied in the d=2 case by Sacks and Uhlenbeck, which opened the door to connecting nonlinear geometric analysis on a manifold to its topology. See math.jhu.edu/~js/Math748/sacks-uhlenbeck.pdf | |
| Mar 26, 2018 at 13:31 | history | asked | Asaf Shachar | CC BY-SA 3.0 |