Timeline for Preferred embedding of finite metric spaces in riemaniann manifolds of given dimension
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2010 at 12:56 | vote | accept | Bruno Galvan | ||
| Oct 14, 2010 at 23:58 | answer | added | Anton Petrunin | timeline score: 6 | |
| Oct 14, 2010 at 23:08 | comment | added | Suresh Venkat | There's an interesting discussion at this question: mathoverflow.net/questions/32527/… on different ways to quantify the complexity of a (Riemannian) metric. That might provide some candidates for your preferred embedding. | |
| Oct 14, 2010 at 21:08 | comment | added | Bruno Galvan | I have in mind that the preferred embedding has something to do with the curvature of the manifold, e.g., in the preferred embedding the manifold has the minimal curvature. This is for example the case of the set with three elements. For the moment I do not consider the masses of the particles. | |
| Oct 14, 2010 at 20:14 | answer | added | Suresh Venkat | timeline score: 2 | |
| Oct 14, 2010 at 19:37 | comment | added | Richard Montgomery | Do you have any thoughts, or suggested axiomatics on what ``preferred'' might mean? Do you want your points to have masses? Gromov has, somewhere, (perhaps in `Metric Structures') some results about embeddings of 4 point spaces that may be of use. | |
| Oct 14, 2010 at 19:29 | comment | added | j.c. | A question about isometrically embedding finite metric spaces into Euclidean spaces is here: mathoverflow.net/questions/12394/… I don't know if any of the results extend to isometric embeddings into Riemannian manifolds. | |
| Oct 14, 2010 at 18:28 | history | edited | Bruno Galvan | CC BY-SA 2.5 |
edited title
|
| Oct 14, 2010 at 18:19 | history | asked | Bruno Galvan | CC BY-SA 2.5 |