Timeline for "Small" maps from sphere to sphere
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2017 at 13:04 | answer | added | Robert Bryant | timeline score: 11 | |
| Aug 15, 2012 at 19:25 | comment | added | Dan Lee | I don't know anything about this particular problem, but in general it is very difficult to minimize volume in a homotopy class. (Minimizing in a homology class is well understood.) The obvious question would be whether the Hopf fibration is a minimizer in the sense you describe. There is some literature, starting with Gluck-Ziller, giving a variational characterization of the Hopf fibration in terms of the "volume" of the foliation. | |
| Aug 5, 2012 at 19:18 | comment | added | Ryan Budney | Related mathoverflow.net/questions/36108/geometry-of-null-homotopies | |
| Aug 5, 2012 at 13:11 | comment | added | Anton Petrunin | You probably know: if the radius of the second factor goes to zero, then your $f$ becomes harmonic. There many explicit examples of harmonic maps $f:S^{n+k}\to S^n$. Some of them should be very symmetric and so they have good chance to have minimal graph... | |
| Aug 5, 2012 at 8:41 | history | asked | David Feldman | CC BY-SA 3.0 |