Timeline for Chebyshev net in 3D
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 18, 2012 at 18:34 | comment | added | Robert Bryant | I'm sure about the existence of solutions if the initial data $f$ are real-analytic and satisfy the necessary inequalities (which are automatic if the initial data are sufficiently close to the identity. I don't know about the existence if the initial data $f$ are only smooth. For this, you would need to check whether the system satisfies the 'generalized symmetric hyperbolic' condition, a thing about which Yang and DeTurck (among others) are expert. (I'd have to go look up the condition, but I don't have the necessary references handy.) | |
| Mar 18, 2012 at 18:11 | comment | added | Anton Petrunin | Thank you. Do I understand right that you are sure about existence of solution. If "yes", maybe you could suggest me something to read? Also do you think higher dimensional nets can be also constructed this way? (You are right, the solution should be unique up to reflection in $\mathbb W^2$.) | |
| Mar 18, 2012 at 17:54 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added some remarks
|
| Mar 18, 2012 at 14:53 | history | answered | Robert Bryant | CC BY-SA 3.0 |