Timeline for Does harmonic map heat flow of a curve always fully converge to a geodesic?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2018 at 18:04 | vote | accept | Ryan Unger | ||
| Oct 4, 2018 at 14:47 | answer | added | Willie Wong | timeline score: 11 | |
| Oct 4, 2018 at 14:27 | comment | added | Willie Wong | According to Råde (in his Yang-Mills heat equation paper), when $(M,g)$ is real analytic this can be derived from Leon Simon's 83 paper jstor.org/stable/2006981?seq=1#metadata_info_tab_contents // incidentally, a related question has been asked before: mathoverflow.net/questions/134930/… | |
| Oct 3, 2018 at 14:47 | comment | added | Benoît Kloeckner | I did not meant that $u_0$ not being homotopically trivial was a necessary condition for the convergence of a subsequence toward a geodesic, but that the later does not hold unconditionally. It seems we agree on this, so that I guess you want to make some assumption on $u_0$. | |
| Oct 3, 2018 at 13:07 | comment | added | Ryan Unger | @BenoîtKloeckner If it's not, then it could shrink to a point. However, it is easy to construct an example where $u_0$ is homotopically nontrivial but converges to a geodesic with positive length. (Think of a dumbbell.) | |
| Oct 3, 2018 at 9:12 | comment | added | Benoît Kloeckner | I guess you mean that $u_0$ is not homotopically trivial, right? | |
| Oct 2, 2018 at 22:23 | history | edited | Ryan Unger | CC BY-SA 4.0 |
added 7 characters in body
|
| Oct 2, 2018 at 22:16 | history | asked | Ryan Unger | CC BY-SA 4.0 |